context
stringlengths
545
71.9k
questionsrc
stringlengths
16
10.2k
question
stringlengths
11
563
in the last video , we introduced ourselves to the law of supply . and it was a fairly common sense idea that if we hold all else equal , that if the price of something goes up , there 's more incentive for more producers to produce it or a given producer to produce more of it . and we saw that . as the price goes up ,...
the more people they are supplying , the higher the supply would be . so if the number of suppliers goes up -- and now you would n't imagine -- this is a curve maybe for the aggregate supply . so if the number of suppliers goes up , then the aggregate supply would go up at any given price point . if the number of suppl...
if there was abnormal profit being made and there were no barriers in entry , then the number of suppliers would increase resulting in lower prices and thus eating into the abnormal profit right ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
3 goes into 24 eight times . 8 times 3 is 24 . no remainder .
for the first problem ... the 4y= -8 ... ... .. where did the -8 came from ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
3 times 3 is 9 . subtract . 10 minus 9 is 1 .
how did you know if you need to add or subtract the numbers ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
i wo n't even write it down . you get 4x minus -- sorry , 4y minus y . that is 3y . and that is going to be equal to $ 2.84 minus $ 1.79 .
but how would you do the work for systems of equations such as , 20=4x+y+2z 18=2x+2y+2z 25=4x+3y+z ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
that 's equal to 7 over 2 . that 's our x value . now we want to solve for our y value .
3x+4y=6 4x+3y=8 just multiply an equation by a negative that makes two of the x or y variables have the same absolute value but opposites ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
now we can substitute back into either of these equations to figure out the cost of a candy bar . so let 's use this bottom equation right here . which was originally , if you remember before i multiplied it by negative 1 , it was 3x plus y is equal to $ 1.79 .
why when finding the y you only use the first equation ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
that 's $ 1.44 . and 3 goes into $ 1.44 , i think it goes -- well , 3 goes into $ 1.44 , it goes into 1 zero times . 1 times 3 is 0 .
how do you know which one goes on which axis ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
3 goes into 10 three times . 3 times 3 is 9 . subtract .
why do you have to substitute the variable into an original equation ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the intersection of the lines that represent the solution sets to both of these equations .
when solving a system of equations using elimination , when you have to multiply one of the equations to get rid of the x or y , how do you know which one you want to get rid of first ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
this is $ 1.79 . how do i know ? because it says this is equal to $ 1.79 .
how do you know whether to eliminate x or y first ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
so how can we proceed ? we saw in substitution , we like to eliminate one of the variables . we did it through substitution last time . but is there anything we can add or subtract -- let 's focus on this yellow , on this top equation right here -- is there anything that we can add or subtract to both sides of this equ...
what is the exact difference between elimination and substitution ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
on the right-hand side , you 're adding 25.5 to the equation . are n't you adding two different things to both sides of the equation ? and my answer would be no .
what do you do if the ys are different ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
the left-hand side -- you 're just left with the 3x ; these cancel out -- is equal to -- let 's see , this is $ 1.79 minus $ 0.35 . that 's $ 1.44 . and 3 goes into $ 1.44 , i think it goes -- well , 3 goes into $ 1.44 , it goes into 1 zero times .
the total number of choir members is 44. how many girls are in the choir ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 .
how do you decide whether to use substitution , multiplication or elimination for systems of equations ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 .
how long does it take for wendy to catch up to wilfred ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
so let 's verify that it also satisfies this bottom equation . 5 times 7/2 is 35 over 2 minus 4 times negative 2 , so minus negative 8 . that 's equivalent to -- let 's see , this is 17.5 plus 8 .
continuing 0 and on , what if you had to substitute `` y '' into the equation 3x+4 ( y ) =2.5 ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
if you just add these two together , they are going to cancel out . they 're going to be plus 0y . or that whole term is just going to go away .
why would the equation be 8x+0y and not be 8x-0y ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
plus 4 times y , the cost of a fruit roll-up . this is how much nadia spends . 3 candy bars , 4 fruit roll-ups .
how much is the bill when the two plans are the same ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
if you just add these two together , they are going to cancel out . they 're going to be plus 0y . or that whole term is just going to go away .
at the beginning , why does sal put an arrow when he is crossing out 0y ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
when you add 3x plus 4y , minus 3x , minus y , the 3x 's cancel out . 3x minus 3x is 0x . i wo n't even write it down . you get 4x minus -- sorry , 4y minus y .
what if i have equations that do n't share a common number of variables , like 3x+6y=6 over 2x-3y=4 ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
what is the cost of each candy bar and each fruit roll-up ? and we 're going to solve this using elimination . you could solve this using any of the techniques we 've seen so far -- substitution , elimination , even graphing , although it 's kind of hard to eyeball things with the graphing .
hey sal , can you solve 3x-2y= -5 and -2x + 5y = 1 using elimination and substitution method ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
so if i were to literally add this to the left-hand side , and add that to the right-hand side . and you 're probably saying , sal , hold on , how can you just add two equations like that ? and remember , when you 're doing any equation , if i have any equation of the form -- well , really , any equation -- ax plus by ...
how do you just add the equation ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
when you add 3x plus 4y , minus 3x , minus y , the 3x 's cancel out . 3x minus 3x is 0x . i wo n't even write it down . you get 4x minus -- sorry , 4y minus y .
hey sal , what if it 's like , i do n't know , 3x+2y=11 over 7x-y=3 ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
and we could substitute this back into either of these two equations . let 's use the top one . you could do it with the bottom one as well .
so even when you use elimination to solve a system of equations you still must use substitution ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
3 times 3 is 9 . subtract . 10 minus 9 is 1 .
how do i know when to add or subtract ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
what is the cost of each candy bar and each fruit roll-up ? and we 're going to solve this using elimination . you could solve this using any of the techniques we 've seen so far -- substitution , elimination , even graphing , although it 's kind of hard to eyeball things with the graphing .
i 'm personally not farmilliar with using fractions in elimination equations , it 's not how i 've been taught in my school curiculum but is the a way to translate the fractions into decimals instead ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
so let 's subtract it . so you get negative 3x minus y -- maybe i should make it very clear this is not a plus sign ; you could imagine i 'm multiplying the second equation by negative 1 -- is equal to negative $ 1.79 . i 'm just taking the second equation .
why would there be a negative sign ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
3 times 3 is 9 . subtract . 10 minus 9 is 1 .
how do you know either to add or subtract ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
let 's just use x and y . let 's let x equal cost of candy bar -- i was going to do a c and a f for fruit roll-up , but i 'll just stick with x and y -- cost of candy bar . and let y equal the cost of a fruit roll-up .
if y=f ( x ) =mx+b , such that f ( 60 ) =429 and f ( 125 ) =884 ; then determine the values of the constant m and b ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
divide both sides by 4 , and you get y is equal to negative 2 . so the solution to this equation is x is equal to 7/2 , y is equal to negative 2 . this would be the coordinate of their intersection .
or does the solution become so fractionated that fractions only make sense ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
3 times 3 is 9 . subtract . 10 minus 9 is 1 .
how do you know to add or subtract equations to eliminate the variable with common coefficient ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
you get 4x minus -- sorry , 4y minus y . that is 3y . and that is going to be equal to $ 2.84 minus $ 1.79 .
what do i do if its something such as 2x+3y=9 and x+5y=8 ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
you get 4x minus -- sorry , 4y minus y . that is 3y . and that is going to be equal to $ 2.84 minus $ 1.79 .
okay so if i had x - 3y = 27 ( over ) 3x - 3y = 39 would you subtract the two ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
it goes into 1 zero times . 0 times 3 is 0 . 1 minus 0 is 1 .
if you had a problem where the variables were n't lined up , so like 0=2y - 4-x and -y=-5x+7 , does elimiation and substition still work ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 .
who create/discovered the linear system ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
and it 's probably not obvious , even though it 's sitting right in front of your face . well , what if we just added this equation to that equation ? what i mean by that is , what if we were to add 5x minus 4y to the left-hand side , and add 25.5 to the right-hand side ?
can you subtract the bottom equation from the top equation ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
and it 's probably not obvious , even though it 's sitting right in front of your face . well , what if we just added this equation to that equation ? what i mean by that is , what if we were to add 5x minus 4y to the left-hand side , and add 25.5 to the right-hand side ?
can you subtract the bottom equation from the top equation ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
and it 's probably not obvious , even though it 's sitting right in front of your face . well , what if we just added this equation to that equation ? what i mean by that is , what if we were to add 5x minus 4y to the left-hand side , and add 25.5 to the right-hand side ?
can you subtract the bottom equation from the top equation ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
remember , any time you deal with an equation you have to add or subtract the same thing to both sides . but is there anything that we could add or subtract to both sides of this equation that might eliminate one of the variables ? and then we would have one equation in one variable , and we can solve for it . and it '...
is it possible to have a negative number once you have subtracted one equation from another in order to eliminate a variable ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 .
why is it necessary for systems of equations ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the intersection of the lines that represent the solution sets to both of these equations .
my problem says : how many solutions ( x , y ) are there to the system of equations ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
so this satisfies both equations . now let 's see if we can use our newly found skills to tackle a word problem , our newly found skills in elimination . so here it says , nadia and peter visit the candy store .
when do you decide to use substitution or elimination method on word problems ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
so let 's verify that it also satisfies this bottom equation . 5 times 7/2 is 35 over 2 minus 4 times negative 2 , so minus negative 8 . that 's equivalent to -- let 's see , this is 17.5 plus 8 .
how did sal get from 5/2 to -21/2 and then to -16/2 ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
and that indeed does equal 25.5 . so this satisfies both equations . now let 's see if we can use our newly found skills to tackle a word problem , our newly found skills in elimination .
how do you solve equations with fractional variables ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
so let 's verify that it also satisfies this bottom equation . 5 times 7/2 is 35 over 2 minus 4 times negative 2 , so minus negative 8 . that 's equivalent to -- let 's see , this is 17.5 plus 8 .
so my teacher gave us homework and i do n't understand it , its `` solving systems my elimination # 2 '' example ; 2x + 2y = -2 5x - 12y = 10 can someone please help ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
now we can substitute back into either of these equations to figure out the cost of a candy bar . so let 's use this bottom equation right here . which was originally , if you remember before i multiplied it by negative 1 , it was 3x plus y is equal to $ 1.79 .
what is the bottom equation doesnt have the same coefficient ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
what is the cost of each candy bar and each fruit roll-up ? and we 're going to solve this using elimination . you could solve this using any of the techniques we 've seen so far -- substitution , elimination , even graphing , although it 's kind of hard to eyeball things with the graphing .
hey sal , how would i solve systems of equations using elimination if one of the variables is isolated ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
3 goes into 10 three times . 3 times 3 is 9 . subtract .
what are the 3 steps of elemination ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
if we were to add the left-hand side , 3x plus 5x is 8x . and then what is 4y minus 4y ? and this was the whole point .
why are the 4y 's being canceled out when your adding ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 .
what is the mass of the empty bucket ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 .
can you use elimination and substitution for systems with more than two equations ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
this is $ 1.79 . how do i know ? because it says this is equal to $ 1.79 .
how would you know when to use elimination or substitution ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
what is the cost of each candy bar and each fruit roll-up ? and we 're going to solve this using elimination . you could solve this using any of the techniques we 've seen so far -- substitution , elimination , even graphing , although it 's kind of hard to eyeball things with the graphing .
how would you solve 5x + 7y = 77 and 5x+3y =53 by using elimination ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
are n't you adding two different things to both sides of the equation ? and my answer would be no . we know that 5x minus 4y is 25.5 .
why would you put the anwser in fraction form ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 .
what is the speed of the plane in still ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 .
what is the speed of the wind ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
no remainder . so x is equal to 0.48 . so there you have it .
( x-4 ) 2 sec power=16 , i believe the x is 8,0 , but when the solution is irrational how do i find this ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
are n't you adding two different things to both sides of the equation ? and my answer would be no . we know that 5x minus 4y is 25.5 .
how would you explain a problem in which the answer is no solution when solving a system of equations using elimination ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
so if i were to literally add this to the left-hand side , and add that to the right-hand side . and you 're probably saying , sal , hold on , how can you just add two equations like that ? and remember , when you 're doing any equation , if i have any equation of the form -- well , really , any equation -- ax plus by ...
what is the app or software that sal uses ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
it goes into 1 zero times . 0 times 3 is 0 . 1 minus 0 is 1 .
why does the y equal 0 ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
that 's equal to 7 over 2 . that 's our x value . now we want to solve for our y value .
hey sal , i am having trouble with the problem : -4x-15y=-17 -x+5y= -13 can you help ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
so how can we proceed ? we saw in substitution , we like to eliminate one of the variables . we did it through substitution last time .
say the eqation is x - 10y = 19 14x - 9y = 20 how do you isolate one of the variables ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
0 times 3 is 0 . 1 minus 0 is 1 . bring down a 0 .
how do you solve the system y=1/2x-1 and 3x-y=-4 ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
so plus 1 additional fruit roll-up . his purchase cost is equal to $ 1.79 . what is the cost of each candy bar and each fruit roll-up ?
how would i find when daves ' total cost be equal to joe 's total cost ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
so if i were to literally add this to the left-hand side , and add that to the right-hand side . and you 're probably saying , sal , hold on , how can you just add two equations like that ? and remember , when you 're doing any equation , if i have any equation of the form -- well , really , any equation -- ax plus by ...
would we always add the two equations when using elimination ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
what is the cost of each candy bar and each fruit roll-up ? and we 're going to solve this using elimination . you could solve this using any of the techniques we 've seen so far -- substitution , elimination , even graphing , although it 's kind of hard to eyeball things with the graphing .
can you solve inequalities using elimination and how does that work ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
but is there anything that we could add or subtract to both sides of this equation that might eliminate one of the variables ? and then we would have one equation in one variable , and we can solve for it . and it 's probably not obvious , even though it 's sitting right in front of your face .
how would you solve an equation like : v= 9/5mpr when you are solving for r ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
so we know that 3 times x , 3 times 7 over 2 -- i 'm just substituting the x value we figured out into this top equation -- 3 times 7 over 2 , plus 4y is equal to 2.5 . let me just write that as 5/2 . we 're going to stay in the fraction world .
write linear system to find number of workers employed at each wage ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
bring down a 0 . 3 goes into 10 three times . 3 times 3 is 9 . subtract .
what would we do if i need to find something out when given three separate equations with 3 variables ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
and that indeed does equal 25.5 . so this satisfies both equations . now let 's see if we can use our newly found skills to tackle a word problem , our newly found skills in elimination .
how would you eliminate with equations with fractions ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
now we want to solve for our y value . and we could substitute this back into either of these two equations . let 's use the top one .
wait- so what does one do if the y-intercept does not get canceled out when adding the two equations together ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
so how can we proceed ? we saw in substitution , we like to eliminate one of the variables . we did it through substitution last time . but is there anything we can add or subtract -- let 's focus on this yellow , on this top equation right here -- is there anything that we can add or subtract to both sides of this equ...
what is the exact difference between substitution and elimination ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 .
when solving a systems equation by elimination can you change both equations ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
this is $ 1.79 . how do i know ? because it says this is equal to $ 1.79 .
like i know how to do this now but if you cant graph this how would you do y=mx+b ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
remember , any time you deal with an equation you have to add or subtract the same thing to both sides . but is there anything that we could add or subtract to both sides of this equation that might eliminate one of the variables ? and then we would have one equation in one variable , and we can solve for it . and it '...
what of one equation is in y=mx+b form ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
3 times 3 is 9 . subtract . 10 minus 9 is 1 .
how do you know when to add or subtract the two equations ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
subtract . bring down the 4 . 3 goes into 14 four times .
if the partnership raised $ 328,000 , then how many investors contributed $ 4,000 and how many contributed $ 8,000 ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
3 goes into 10 three times . 3 times 3 is 9 . subtract .
what would happen if we did n't cancel out all of the y 's 2?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
3 times 3 is 9 . subtract . 10 minus 9 is 1 .
how do you know when to add and when to subtract ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
so let 's verify that it also satisfies this bottom equation . 5 times 7/2 is 35 over 2 minus 4 times negative 2 , so minus negative 8 . that 's equivalent to -- let 's see , this is 17.5 plus 8 .
what if i have 9x+y=2 -4x-y=-17 what do i do when the x is negative ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
this is $ 1.79 . how do i know ? because it says this is equal to $ 1.79 .
how do you know when to do substation or multiplication or elimination ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
what is the cost of each candy bar and each fruit roll-up ? and we 're going to solve this using elimination . you could solve this using any of the techniques we 've seen so far -- substitution , elimination , even graphing , although it 's kind of hard to eyeball things with the graphing .
are there any other methods to solve simultaneous equations besides substitution and elimination ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
but is there anything that we could add or subtract to both sides of this equation that might eliminate one of the variables ? and then we would have one equation in one variable , and we can solve for it . and it 's probably not obvious , even though it 's sitting right in front of your face .
does a variable have to be a letter ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
you could do it with the bottom one as well . so we know that 3 times x , 3 times 7 over 2 -- i 'm just substituting the x value we figured out into this top equation -- 3 times 7 over 2 , plus 4y is equal to 2.5 . let me just write that as 5/2 .
how would you solve x/2 -1y/3=-7 and x/3+2/3y=10/3 using the elimination method ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
the left-hand side -- you 're just left with the 3x ; these cancel out -- is equal to -- let 's see , this is $ 1.79 minus $ 0.35 . that 's $ 1.44 . and 3 goes into $ 1.44 , i think it goes -- well , 3 goes into $ 1.44 , it goes into 1 zero times .
what does the equation ax+by=c represent ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
and it 's probably not obvious , even though it 's sitting right in front of your face . well , what if we just added this equation to that equation ? what i mean by that is , what if we were to add 5x minus 4y to the left-hand side , and add 25.5 to the right-hand side ?
is it kind of like the equation y=mx+b in finding the slope ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
now we want to solve for our y value . and we could substitute this back into either of these two equations . let 's use the top one .
my question is , if one of the equations had a third variable , for example : x + y + z = b x + y = a can these two equations still be added together like the two in video , even though there is an extra variable involved ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
that 's our x value . now we want to solve for our y value . and we could substitute this back into either of these two equations .
what if we have : 2x-5y=11 4x+10y=18 how can i solve it ?
let 's explore a few more methods for solving systems of equations . let 's say i have the equation , 3x plus 4y is equal to 2.5 . and i have another equation , 5x minus 4y is equal to 25.5 . and we want to find an x and y value that satisfies both of these equations . if you think of it graphically , this would be the...
so you get 8x is equal to 28 . and you divide both sides by 8 , and we get x is equal to 28 over 8 , or you divide the numerator and the denominator by 4 . that 's equal to 7 over 2 .
so to solve : 2x-3y=4 4x-6y=8 wouldnt you have to multiply or divide ?
we are asked to evaluate the expression five to the x power minus three to the x power for x equals two . so pause this video , and see if you can figure out , what does this expression equal when x equals two ? all right , now let 's work through this together . so what we want to do is everywhere we see an x , we wa...
we are asked to evaluate the expression five to the x power minus three to the x power for x equals two . so pause this video , and see if you can figure out , what does this expression equal when x equals two ?
what is ( x+4 ) ^2 = 25x^2 ?
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an...
let 's actually get to the theorem . so fc is parallel to ab , [ ? able ? ]
so ... is ab and fc equal ?
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an...
and we know if two triangles have two angles that are the same , actually the third one 's going to be the same as well . or you could say by the angle-angle similarity postulate , these two triangles are similar . so let me write that down .
based on this information , would n't the angle-side-angle postulate tell us that any two triangles formed from an angle bisector are congruent ?
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an...
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here .
if triangle bcf is isosceles , should n't triangle abc be isosceles too ?
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an...
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here .
does n't that make triangle abc isosceles ?
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an...
so now that we know they 're similar , we know the ratio of ab to ad is going to be equal to -- and we could even look here for the corresponding sides . the ratio of ab , the corresponding side is going to be cf -- is going to equal cf over ad . ad is the same thing as cd -- over cd .
my question is that for example if side ab is longer than side bc , would n't cf be longer than bc ?
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an...
and we could have done it with any of the three angles , but i 'll just do this one . i 'll make our proof a little bit easier . so i 'm just going to bisect this angle , angle abc .
can somebody please give me some hints as to how to make successful proofs ?
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an...
we know that these two angles are congruent to each other , but we do n't know whether this angle is equal to that angle or that angle . we do n't know . we ca n't make any statements like that .
how do i know when to use what proof for what problem ?
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an...
i 'll make our proof a little bit easier . so i 'm just going to bisect this angle , angle abc . so let 's just say that 's the angle bisector of angle abc , and so this angle right over here is equal to this angle right over here . and let me call this point down here -- let me call it point d. the angle bisector theo...
can someone please simply state the angle bisector theorem ?
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an...
you want to make sure you get the corresponding sides right . we now know by angle-angle -- and i 'm going to start at the green angle -- that triangle b -- and then the blue angle -- bda is similar to triangle -- so then once again , let 's start with the green angle , f. then , you go to the blue angle , fdc . and he...
in the diagram of the triangle in does line bd cut through the triangle in such a way that line ad is equal to line cd , because angle abd is congruent to angle cbd ?
what i want to do first is just show you what the angle bisector theorem is and then we 'll actually prove it for ourselves . so i just have an arbitrary triangle right over here , triangle abc . and what i 'm going to do is i 'm going to draw an angle bisector for this angle up here . and we could have done it with an...
i 'll make our proof a little bit easier . so i 'm just going to bisect this angle , angle abc . so let 's just say that 's the angle bisector of angle abc , and so this angle right over here is equal to this angle right over here . and let me call this point down here -- let me call it point d. the angle bisector theo...
does that mean the angle bisector theorem does not work on scalene triangles ?