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help-1
8b04c92fe27c4ec48854d270088b60ff
456,226,577,798,135,800
Deleted User
12/22/2021 10:30:57
is this provable graphically (that this is always the case?)
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8b04c92fe27c4ec48854d270088b60ff
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<><><>
12/22/2021 10:38:25
Ohh. I get your question. Hmm, it appears to be so. As for a proof, maybe big brain ann can help @Ann
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8b04c92fe27c4ec48854d270088b60ff
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Ann
12/22/2021 10:38:36
nyeh?
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8b04c92fe27c4ec48854d270088b60ff
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Ann
12/22/2021 10:38:46
oh
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Ann
12/22/2021 10:38:46
this
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8b04c92fe27c4ec48854d270088b60ff
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Ann
12/22/2021 10:38:52
i don't have the energy for this sorry
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help-1
8b04c92fe27c4ec48854d270088b60ff
691,679,326,164,222,100
Euclid31415
12/22/2021 13:54:59
Solutions to your quartic in y are +-3 and +-√(-20). Since "y" was taken to be a real number, solutions +-√(-20) are discarded.
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8b04c92fe27c4ec48854d270088b60ff
691,679,326,164,222,100
Euclid31415
12/22/2021 13:57:31
From 2xy=12√5, y=3 gives us x=2√5 and y=-3 gives x=-2√5
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8b04c92fe27c4ec48854d270088b60ff
456,226,577,798,135,800
Deleted User
12/22/2021 14:30:33
My question isn't about solutions
1
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205,698
help-1
8b04c92fe27c4ec48854d270088b60ff
456,226,577,798,135,800
Deleted User
12/22/2021 14:30:51
It's about why the second solution is the value of the corresponding variable
1
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help-1
8b04c92fe27c4ec48854d270088b60ff
691,679,326,164,222,100
Euclid31415
12/22/2021 14:31:46
Wdym "second solution"? And you do know that finding the solution here means finding the values of x,y, such that the equations are satisfied right?
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8b04c92fe27c4ec48854d270088b60ff
691,679,326,164,222,100
Euclid31415
12/22/2021 14:42:26
You could solve for x first and then find the values of y from there it doesn't matter
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help-1
8b04c92fe27c4ec48854d270088b60ff
700,047,727,366,635,500
Tøøthpick
12/22/2021 14:42:57
https://cdn.discordapp.c…FDAFFDB59EEE.jpg
7B2EF9CD-4837-4953-B088-FDAFFDB59EEE.jpg
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8b04c92fe27c4ec48854d270088b60ff
700,047,727,366,635,500
Tøøthpick
12/22/2021 14:43:03
Can anyone help me with that
0
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help-1
8b04c92fe27c4ec48854d270088b60ff
700,047,727,366,635,500
Tøøthpick
12/22/2021 14:43:33
?
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help-1
8b04c92fe27c4ec48854d270088b60ff
691,679,326,164,222,100
Euclid31415
12/22/2021 14:43:35
Post in an unoccupied channel. Read #❓how-to-get-help
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8b04c92fe27c4ec48854d270088b60ff
456,226,577,798,135,800
Deleted User
12/22/2021 15:01:58
When finding values of y, you also get complex roots for y
1
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205,698
help-1
8b04c92fe27c4ec48854d270088b60ff
456,226,577,798,135,800
Deleted User
12/22/2021 15:02:08
Those complex roots correspond to the values of x
1
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help-1
8b04c92fe27c4ec48854d270088b60ff
456,226,577,798,135,800
Deleted User
12/22/2021 15:02:23
My question was if this is always true and if there is a graphical proof
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8b04c92fe27c4ec48854d270088b60ff
691,679,326,164,222,100
Euclid31415
12/22/2021 18:31:23
No they don't. The values of x we get are +-√20 which is not related to the imaginary values +-i√20 we get while solving for y.
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help-1
8b04c92fe27c4ec48854d270088b60ff
456,226,577,798,135,800
Deleted User
12/22/2021 18:32:52
the root(-20) is the x value
1
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8b04c92fe27c4ec48854d270088b60ff
456,226,577,798,135,800
Deleted User
12/22/2021 18:33:00
it corresponds to the other value
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8b04c92fe27c4ec48854d270088b60ff
456,226,577,798,135,800
Deleted User
12/22/2021 18:33:05
it done it in every question i did
1
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help-1
8b04c92fe27c4ec48854d270088b60ff
456,226,577,798,135,800
Deleted User
12/22/2021 18:33:22
im tryna find a proof for it to see if it **always** does it
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help-1
8b04c92fe27c4ec48854d270088b60ff
691,679,326,164,222,100
Euclid31415
12/22/2021 18:33:25
root(-20) is not a real number. x was given as a real number
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help-1
8b04c92fe27c4ec48854d270088b60ff
456,226,577,798,135,800
Deleted User
12/22/2021 18:33:32
alright then
1
0
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help-1
8b04c92fe27c4ec48854d270088b60ff
456,226,577,798,135,800
Deleted User
12/22/2021 18:33:36
its the negative of x
1
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205,698
help-1
8b04c92fe27c4ec48854d270088b60ff
456,226,577,798,135,800
Deleted User
12/22/2021 18:33:58
its the variable x multiplied by -i
1
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help-1
8b04c92fe27c4ec48854d270088b60ff
456,226,577,798,135,800
Deleted User
12/22/2021 18:34:13
whatever u wanna call it, its possible to take the other value from it none the less
1
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205,698
help-1
8b04c92fe27c4ec48854d270088b60ff
456,226,577,798,135,800
Deleted User
12/22/2021 18:34:20
and im wondering why this is, graphically what is going on.
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help-1
8b04c92fe27c4ec48854d270088b60ff
691,679,326,164,222,100
Euclid31415
12/22/2021 18:42:11
If you allow the complex values of y from the quartic you got, then the extra solutions you get are y=+-i√(20) and x=-+3i which also does provide us with the square roots of 11+12√5i when we write them in the form x+iy. The fact that we are multiplying i to "y" again transforms +-i√(20) to -+√20 which we need as the re...
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help-1
8b04c92fe27c4ec48854d270088b60ff
691,679,326,164,222,100
Euclid31415
12/22/2021 18:51:23
Because we know that finally, there are exactly two square roots of 11+12√5i namely, √(20)+3i and -√(20)-3i
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help-1
8b04c92fe27c4ec48854d270088b60ff
691,679,326,164,222,100
Euclid31415
12/22/2021 19:02:51
From the solution standpoint, if we have some x=a, y=b satisfying x²-y²=11 and 2xy=12√5 then x=bi, y=-ai also qualifies as a solution
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help-1
8b04c92fe27c4ec48854d270088b60ff
691,679,326,164,222,100
Euclid31415
12/22/2021 19:18:53
All of this stems from the fact that allowing x,y to be either purely real or purely imaginary implies the equation a+bi=x+iy (a,b real) has two pairs of solutions namely x=a, y=b and x=bi, y=-ai
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8b04c92fe27c4ec48854d270088b60ff
691,679,326,164,222,100
Euclid31415
12/22/2021 19:30:23
Graphically, it's not that nice since you can't plot (bi,-ai)
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help-1
8b04c92fe27c4ec48854d270088b60ff
456,226,577,798,135,800
Deleted User
12/22/2021 19:55:23
Uhhhh
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help-1
8b04c92fe27c4ec48854d270088b60ff
456,226,577,798,135,800
Deleted User
12/22/2021 19:56:33
I kinda understand but half don't
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help-1
8b04c92fe27c4ec48854d270088b60ff
456,226,577,798,135,800
Deleted User
12/22/2021 19:56:52
Multiplying I to y. What does that mean?
1
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help-1
8b04c92fe27c4ec48854d270088b60ff
456,226,577,798,135,800
Deleted User
12/22/2021 19:57:26
Also is the conjugate as well as the +- solutions?
1
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help-1
8b04c92fe27c4ec48854d270088b60ff
456,226,577,798,135,800
Deleted User
12/22/2021 19:57:53
The real value can be +- too? Doesn't that mean there is indeed 4 solutions?
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205,698
help-1
8b04c92fe27c4ec48854d270088b60ff
456,226,577,798,135,800
Deleted User
12/22/2021 19:58:41
Your solution standpoint works fine tho thanks
1
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help-1
8b04c92fe27c4ec48854d270088b60ff
456,226,577,798,135,800
Deleted User
12/22/2021 19:58:48
So that proves it's always the case.
1
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help-1
8b04c92fe27c4ec48854d270088b60ff
691,679,326,164,222,100
Euclid31415
12/22/2021 20:02:32
No. Conjugates have nothing to do with this.
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help-1
8b04c92fe27c4ec48854d270088b60ff
691,679,326,164,222,100
Euclid31415
12/22/2021 20:05:39
There are only two squareroots of 11+12√5i in the end. Allowing x,y to be either purely real or purely imaginary gives us 4 pairs of solutions (x,y) for 11+12√5i=(x+iy)^2
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help-1
8b04c92fe27c4ec48854d270088b60ff
456,226,577,798,135,800
Deleted User
12/23/2021 03:45:24
Gonna thjnj about it iab
1
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help-1
8b04c92fe27c4ec48854d270088b60ff
456,226,577,798,135,800
Deleted User
12/23/2021 07:48:16
.close
1
0
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help-1
a890ca2139e041be98772204f4d231f4
677,350,243,293,069,300
aab
01/28/2022 05:24:56
Hello, I tried two approaches but ended up with two different answers. Now I can’t continue cause I don’t know which one is correct
1
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help-1
a890ca2139e041be98772204f4d231f4
677,350,243,293,069,300
aab
01/28/2022 05:25:01
https://cdn.discordapp.c…627/IMG_2652.jpg
IMG_2652.jpg
1
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help-1
a890ca2139e041be98772204f4d231f4
706,934,233,012,371,600
Ansh_
01/28/2022 05:26:22
What was the integral btw? because your expression and your first steps don't match
0
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help-1
a890ca2139e041be98772204f4d231f4
706,934,233,012,371,600
Ansh_
01/28/2022 05:26:41
Maybe a mistake in copying the question right
0
1
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help-1
a890ca2139e041be98772204f4d231f4
677,350,243,293,069,300
aab
01/28/2022 05:27:36
$\int \frac {2sec^{2}\theta d\theta } {(2sec\theta)^{4}}$
1
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help-1
a890ca2139e041be98772204f4d231f4
510,789,298,321,096,700
TeXit
01/28/2022 05:28:56
**aIex**
https://cdn.discordapp.c…243293069312.png
677350243293069312.png
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help-1
a890ca2139e041be98772204f4d231f4
706,934,233,012,371,600
Ansh_
01/28/2022 05:29:04
Ah that makes much more sense
0
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help-1
a890ca2139e041be98772204f4d231f4
677,350,243,293,069,300
aab
01/28/2022 05:29:09
yep
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help-1
a890ca2139e041be98772204f4d231f4
706,934,233,012,371,600
Ansh_
01/28/2022 05:29:59
$\frac{2}{16}\int \frac {sec^{2}\theta} {(sec\theta)^{4}} \dd{\theta}$
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help-1
a890ca2139e041be98772204f4d231f4
510,789,298,321,096,700
TeXit
01/28/2022 05:30:01
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
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205,699
help-1
a890ca2139e041be98772204f4d231f4
677,350,243,293,069,300
aab
01/28/2022 05:30:14
yep
1
0
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help-1
a890ca2139e041be98772204f4d231f4
706,934,233,012,371,600
Ansh_
01/28/2022 05:30:37
Are you allowed to do substitution? Or are you doing it without substitution?
0
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help-1
a890ca2139e041be98772204f4d231f4
677,350,243,293,069,300
aab
01/28/2022 05:32:05
allowed
1
0
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help-1
a890ca2139e041be98772204f4d231f4
706,934,233,012,371,600
Ansh_
01/28/2022 05:33:02
btw $\frac{1}{8}\int \frac {1} {\sec^{2}\theta} \dd{\theta} = \frac{1}{8}\int \frac {1} {\underbrace{\tan^{2}\theta +1}} \dd{\theta}$ is not actually what you'd want to do. I'd suggest using sec cos relation
0
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help-1
a890ca2139e041be98772204f4d231f4
677,350,243,293,069,300
aab
01/28/2022 05:34:09
ohh okay
1
0
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help-1
a890ca2139e041be98772204f4d231f4
510,789,298,321,096,700
TeXit
01/28/2022 05:34:22
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
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205,699
help-1
a890ca2139e041be98772204f4d231f4
706,934,233,012,371,600
Ansh_
01/28/2022 05:34:24
@aab:this: ~~sorry ale, wrong ping~~
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help-1
a890ca2139e041be98772204f4d231f4
677,350,243,293,069,300
aab
01/28/2022 05:35:09
imma make it cos^2(theta) instead?
1
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716,505,727,367,249,900
your brother
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205,699
help-1
a890ca2139e041be98772204f4d231f4
706,934,233,012,371,600
Ansh_
01/28/2022 05:35:15
Yeah
0
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help-1
a890ca2139e041be98772204f4d231f4
706,934,233,012,371,600
Ansh_
01/28/2022 05:35:24
and integrate cos^2(theta)
0
1
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205,699
help-1
a890ca2139e041be98772204f4d231f4
677,350,243,293,069,300
aab
01/28/2022 05:36:25
okay cool imma work on it and come back if i got some troubles
1
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help-1
a890ca2139e041be98772204f4d231f4
677,350,243,293,069,300
aab
01/28/2022 05:43:49
ok i think i got it now. thanks @Ansh_ !!
1
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help-1
a890ca2139e041be98772204f4d231f4
706,934,233,012,371,600
Ansh_
01/28/2022 05:43:57
:D
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help-1
a890ca2139e041be98772204f4d231f4
706,934,233,012,371,600
Ansh_
01/28/2022 05:44:04
> .close before you leave
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help-1
a890ca2139e041be98772204f4d231f4
677,350,243,293,069,300
aab
01/28/2022 05:59:04
.close
1
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help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 06:33:25
https://cdn.discordapp.c…0690/unknown.png
unknown.png
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help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 06:33:56
I don't understand this almost at all
1
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help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 06:34:32
Solving for m simultaneously yields me `m = 1` or `m = -3` but I don't know how that plays into "infinitely many solutions" and "no solutions"
1
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null
205,700
help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 06:36:49
Context: New school, some unfamiliar content, I don't understand the single example provided in the textbook (too vague)
1
0
null
null
null
null
null
205,700
help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 06:37:03
okay
0
1
null
null
null
null
null
205,700
help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 06:37:06
let’s think about it
0
1
null
null
null
null
null
205,700
help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 06:37:17
these two equations
0
1
null
null
null
null
null
205,700
help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 06:37:20
what are they?
0
1
null
null
null
null
null
205,700
help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 06:37:27
Straight lines
1
0
null
null
null
null
null
205,700
help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 06:37:31
yep
0
1
null
null
null
null
null
205,700
help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 06:37:33
Can be rearranged into y=mx+c
1
0
259,180,275,345,391,600
barrelbarrelbarrel
1229
barrelbarrelbarrel
false
205,700
help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 06:37:45
true
0
1
null
null
null
null
null
205,700
help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 06:37:50
they can also be in the form of
0
1
null
null
null
null
null
205,700
help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 06:37:55
ax+by+c=0
0
1
null
null
null
null
null
205,700
help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 06:37:59
but anyway
0
1
null
null
null
null
null
205,700
help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 06:38:14
if two lines have infinitely many solutions
0
1
null
null
null
null
null
205,700
help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 06:38:23
what does that say about the relation between these lines?
0
1
null
null
null
null
null
205,700
help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 06:38:37
That's where I'm stuck
1
0
null
null
null
null
null
205,700
help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 06:38:44
I'm not entirely sure what a "solution" here is
1
0
null
null
null
null
null
205,700
help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 06:39:15
for example we have the lines x+2y+3=0 and 2x+3y+5=0
0
1
null
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null
null
null
205,700
help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 06:39:40
is there at least a pair of (x,y) that’ll satisfy both linear equations?
0
1
null
null
null
null
null
205,700
help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 06:39:54
in what case will there be no (x,y) pairs?
0
1
null
null
null
null
null
205,700
help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 06:40:03
Right gotcha
1
0
null
null
null
null
null
205,700
help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 06:40:40
So it's asking what value of *m* allows infinite x and y solutions?
1
0
null
null
null
null
null
205,700
help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 06:40:52
yep
0
1
null
null
null
null
null
205,700
help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 06:41:00
Alright
1
0
null
null
null
null
null
205,700
help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 06:41:10
but now think about two lines
0
1
null
null
null
null
null
205,700
help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 06:41:20
when you input any x value
0
1
null
null
null
null
null
205,700
help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 06:41:29
they’ll output the same y value
0
1
null
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null