input
stringlengths
13
66
output
stringlengths
30
276
Find x and y such that 7x + 3y = -361/63 2x + 4y = -584/63
7x + 3y = -361/63 2x + 4y = -584/63 Using elimination 2*(7x + 3y = -361/63) 7*(2x + 4y = -584/63) 14x + 6y = -722/63 14x + 28y = -584/9 Subtract equations -22y = 374/7 y = 374/7/-22 y = -17/7 Substitute y 7x + 3(-17/7) = -361/63 7x = 14/9 x = 14/9/7 x = 2/9
What value of x satisfies x^2 + 157/8x - 15/2 = 0
x^2 + 157/8x - 15/2 = 0 (x - 3/8)(x - -20) = 0 x - 3/8 = 0 or x - -20 = 0 x = 3/8 x = -20
Find the solution to 7x - 56/5 = 0
7x - 56/5 = 0 7x = 56/5 x = 56/5 / 7 x = 8/5
Solve the system: 3x + 6y = -173/21 6x + 1y = -730/63
3x + 6y = -173/21 6x + 1y = -730/63 Using elimination 6*(3x + 6y = -173/21) 3*(6x + 1y = -730/63) 18x + 36y = -346/7 18x + 3y = -730/21 Subtract equations 33y = -44/3 y = -44/3/33 y = -4/9 Substitute y 3x + 6(-4/9) = -173/21 3x = -39/7 x = -39/7/3 x = -13/7
Solve simultaneously: 10x + 6y = 130/9 1x + 1y = 25/9
10x + 6y = 130/9 1x + 1y = 25/9 Using elimination 1*(10x + 6y = 130/9) 10*(1x + 1y = 25/9) 10x + 6y = 130/9 10x + 10y = 250/9 Subtract equations -4y = -40/3 y = -40/3/-4 y = 10/3 Substitute y 10x + 6(10/3) = 130/9 10x = -50/9 x = -50/9/10 x = -5/9
Solve the equations: 8x + 2y = 38 1x + 9y = 719/4
8x + 2y = 38 1x + 9y = 719/4 Using elimination 1*(8x + 2y = 38) 8*(1x + 9y = 719/4) 8x + 2y = 38 8x + 72y = 1438 Subtract equations -70y = -1400 y = -1400/-70 y = 20 Substitute y 8x + 2(20) = 38 8x = -2 x = -2/8 x = -1/4
Find x for 10x + 20/3 = 0
10x + 20/3 = 0 10x = -20/3 x = -20/3 / 10 x = -2/3
Find x for 6x - 51/2 = 0
6x - 51/2 = 0 6x = 51/2 x = 51/2 / 6 x = 17/4
Solve the equations: 6x + 9y = -48/5 5x + 5y = -11/2
6x + 9y = -48/5 5x + 5y = -11/2 Using elimination 5*(6x + 9y = -48/5) 6*(5x + 5y = -11/2) 30x + 45y = -48 30x + 30y = -33 Subtract equations 15y = -15 y = -15/15 y = -1 Substitute y 6x + 9(-1) = -48/5 6x = -3/5 x = -3/5/6 x = -1/10
Solve 1x + 5/9 = 0
1x + 5/9 = 0 1x = -5/9 x = -5/9 / 1 x = -5/9
Find the solution to x^3 + 11/12x^2 - 19/8x - 15/8 = 0
x^3 + 11/12x^2 - 19/8x - 15/8 = 0 (x - -3/4)(x - 3/2)(x - -5/3) = 0 x - -3/4 = 0 x - 3/2 = 0 x - -5/3 = 0 x = -3/4 x = 3/2 x = -5/3
Solve quickly: x^3 + 159/8x^2 + 285/32x - 4693/32 = 0
x^3 + 159/8x^2 + 285/32x - 4693/32 = 0 (x - -13/4)(x - -19)(x - 19/8) = 0 x - -13/4 = 0 x - -19 = 0 x - 19/8 = 0 x = -13/4 x = -19 x = 19/8
Find x and y such that 10x + 10y = -75/2 10x + 7y = -33
10x + 10y = -75/2 10x + 7y = -33 Using elimination 10*(10x + 10y = -75/2) 10*(10x + 7y = -33) 100x + 100y = -375 100x + 70y = -330 Subtract equations 30y = -45 y = -45/30 y = -3/2 Substitute y 10x + 10(-3/2) = -75/2 10x = -45/2 x = -45/2/10 x = -9/4
Determine x in x^2 - 3x - 10 = 0
x^2 - 3x - 10 = 0 (x - 5)(x - -2) = 0 x - 5 = 0 or x - -2 = 0 x = 5 x = -2
What value of x satisfies x^3 - 49/10x^2 + 72/5 = 0
x^3 - 49/10x^2 + 72/5 = 0 (x - -3/2)(x - 4)(x - 12/5) = 0 x - -3/2 = 0 x - 4 = 0 x - 12/5 = 0 x = -3/2 x = 4 x = 12/5
Solve the system: 9x + 10y = -109/4 1x + 8y = -53/3
9x + 10y = -109/4 1x + 8y = -53/3 Using elimination 1*(9x + 10y = -109/4) 9*(1x + 8y = -53/3) 9x + 10y = -109/4 9x + 72y = -159 Subtract equations -62y = 527/4 y = 527/4/-62 y = -17/8 Substitute y 9x + 10(-17/8) = -109/4 9x = -6 x = -6/9 x = -2/3
What value of x satisfies x^3 - 24/5x^2 + 3x + 4/5 = 0
x^3 - 24/5x^2 + 3x + 4/5 = 0 (x - -1/5)(x - 4)(x - 1) = 0 x - -1/5 = 0 x - 4 = 0 x - 1 = 0 x = -1/5 x = 4 x = 1
Solve the system: 10x + 9y = -30 5x + 9y = -20
10x + 9y = -30 5x + 9y = -20 Using elimination 5*(10x + 9y = -30) 10*(5x + 9y = -20) 50x + 45y = -150 50x + 90y = -200 Subtract equations -45y = 50 y = 50/-45 y = -10/9 Substitute y 10x + 9(-10/9) = -30 10x = -20 x = -20/10 x = -2
Compute the solution of 4x - 20/3 = 0
4x - 20/3 = 0 4x = 20/3 x = 20/3 / 4 x = 5/3
Solve the equation x^2 + 19/8x + 21/16 = 0
x^2 + 19/8x + 21/16 = 0 (x - -7/8)(x - -3/2) = 0 x - -7/8 = 0 or x - -3/2 = 0 x = -7/8 x = -3/2
Solve simultaneously: 2x + 3y = 7/2 5x + 3y = 71/4
2x + 3y = 7/2 5x + 3y = 71/4 Using elimination 5*(2x + 3y = 7/2) 2*(5x + 3y = 71/4) 10x + 15y = 35/2 10x + 6y = 71/2 Subtract equations 9y = -18 y = -18/9 y = -2 Substitute y 2x + 3(-2) = 7/2 2x = 19/2 x = 19/2/2 x = 19/4
Solve quickly: 3x + 42 = 0
3x + 42 = 0 3x = -42 x = -42 / 3 x = -14
Solve quickly: 3x + 7 = 0
3x + 7 = 0 3x = -7 x = -7 / 3 x = -7/3
Solve the equations: 10x + 1y = -335/9 6x + 2y = -956/45
10x + 1y = -335/9 6x + 2y = -956/45 Using elimination 6*(10x + 1y = -335/9) 10*(6x + 2y = -956/45) 60x + 6y = -670/3 60x + 20y = -1912/9 Subtract equations -14y = -98/9 y = -98/9/-14 y = 7/9 Substitute y 10x + 1(7/9) = -335/9 10x = -38 x = -38/10 x = -19/5
Determine x in 9x + 81/10 = 0
9x + 81/10 = 0 9x = -81/10 x = -81/10 / 9 x = -9/10
Find x and y such that 10x + 7y = 76 3x + 1y = 64/3
10x + 7y = 76 3x + 1y = 64/3 Using elimination 3*(10x + 7y = 76) 10*(3x + 1y = 64/3) 30x + 21y = 228 30x + 10y = 640/3 Subtract equations 11y = 44/3 y = 44/3/11 y = 4/3 Substitute y 10x + 7(4/3) = 76 10x = 200/3 x = 200/3/10 x = 20/3
Solve the equations: 3x + 4y = 45/2 1x + 1y = 13/2
3x + 4y = 45/2 1x + 1y = 13/2 Using elimination 1*(3x + 4y = 45/2) 3*(1x + 1y = 13/2) 3x + 4y = 45/2 3x + 3y = 39/2 Subtract equations 1y = 3 y = 3/1 y = 3 Substitute y 3x + 4(3) = 45/2 3x = 21/2 x = 21/2/3 x = 7/2
Solve x^2 - 9x - 90 = 0
x^2 - 9x - 90 = 0 (x - -6)(x - 15) = 0 x - -6 = 0 or x - 15 = 0 x = -6 x = 15
Find x for x^3 + 173/18x^2 - 371/9x + 221/6 = 0
x^3 + 173/18x^2 - 371/9x + 221/6 = 0 (x - -13)(x - 3/2)(x - 17/9) = 0 x - -13 = 0 x - 3/2 = 0 x - 17/9 = 0 x = -13 x = 3/2 x = 17/9
Solve the equations: 2x + 3y = -31/7 7x + 5y = -81/7
2x + 3y = -31/7 7x + 5y = -81/7 Using elimination 7*(2x + 3y = -31/7) 2*(7x + 5y = -81/7) 14x + 21y = -31 14x + 10y = -162/7 Subtract equations 11y = -55/7 y = -55/7/11 y = -5/7 Substitute y 2x + 3(-5/7) = -31/7 2x = -16/7 x = -16/7/2 x = -8/7
Find x in 6x + 90/7 = 0
6x + 90/7 = 0 6x = -90/7 x = -90/7 / 6 x = -15/7
Find x in x^3 - 82/7x^2 - 1205/7x + 900/7 = 0
x^3 - 82/7x^2 - 1205/7x + 900/7 = 0 (x - 20)(x - -9)(x - 5/7) = 0 x - 20 = 0 x - -9 = 0 x - 5/7 = 0 x = 20 x = -9 x = 5/7
Find the solution to 5x - 95/4 = 0
5x - 95/4 = 0 5x = 95/4 x = 95/4 / 5 x = 19/4
Solve the equations: 2x + 9y = -67/4 7x + 3y = -343/24
2x + 9y = -67/4 7x + 3y = -343/24 Using elimination 7*(2x + 9y = -67/4) 2*(7x + 3y = -343/24) 14x + 63y = -469/4 14x + 6y = -343/12 Subtract equations 57y = -266/3 y = -266/3/57 y = -14/9 Substitute y 2x + 9(-14/9) = -67/4 2x = -11/4 x = -11/4/2 x = -11/8
Compute the solution of 2x - 3 = 0
2x - 3 = 0 2x = 3 x = 3 / 2 x = 3/2
Solve quickly: x^2 - 16 = 0
x^2 - 16 = 0 (x - 4)(x - -4) = 0 x - 4 = 0 or x - -4 = 0 x = 4 x = -4
Solve quickly: x^2 + 89/40x + 99/80 = 0
x^2 + 89/40x + 99/80 = 0 (x - -9/8)(x - -11/10) = 0 x - -9/8 = 0 or x - -11/10 = 0 x = -9/8 x = -11/10
Find the solution to 7x + 119/8 = 0
7x + 119/8 = 0 7x = -119/8 x = -119/8 / 7 x = -17/8
Solve the equation x^3 + 108/35x^2 + 387/140x + 81/140 = 0
x^3 + 108/35x^2 + 387/140x + 81/140 = 0 (x - -9/7)(x - -3/2)(x - -3/10) = 0 x - -9/7 = 0 x - -3/2 = 0 x - -3/10 = 0 x = -9/7 x = -3/2 x = -3/10
Solve the system: 10x + 3y = 146 8x + 9y = 130
10x + 3y = 146 8x + 9y = 130 Using elimination 8*(10x + 3y = 146) 10*(8x + 9y = 130) 80x + 24y = 1168 80x + 90y = 1300 Subtract equations -66y = -132 y = -132/-66 y = 2 Substitute y 10x + 3(2) = 146 10x = 140 x = 140/10 x = 14
Solve x^3 + 29/45x^2 - 1564/405x - 64/81 = 0
x^3 + 29/45x^2 - 1564/405x - 64/81 = 0 (x - 16/9)(x - -1/5)(x - -20/9) = 0 x - 16/9 = 0 x - -1/5 = 0 x - -20/9 = 0 x = 16/9 x = -1/5 x = -20/9
Find x and y such that 2x + 6y = 29/4 5x + 10y = 95/8
2x + 6y = 29/4 5x + 10y = 95/8 Using elimination 5*(2x + 6y = 29/4) 2*(5x + 10y = 95/8) 10x + 30y = 145/4 10x + 20y = 95/4 Subtract equations 10y = 25/2 y = 25/2/10 y = 5/4 Substitute y 2x + 6(5/4) = 29/4 2x = -1/4 x = -1/4/2 x = -1/8
Compute the solution of 8x - 24 = 0
8x - 24 = 0 8x = 24 x = 24 / 8 x = 3
Find x for x^3 - 163/24x^2 + 233/24x - 15/4 = 0
x^3 - 163/24x^2 + 233/24x - 15/4 = 0 (x - 5)(x - 9/8)(x - 2/3) = 0 x - 5 = 0 x - 9/8 = 0 x - 2/3 = 0 x = 5 x = 9/8 x = 2/3
Determine x in x^3 - 274/9x^2 + 2087/9x - 2470/9 = 0
x^3 - 274/9x^2 + 2087/9x - 2470/9 = 0 (x - 10)(x - 13/9)(x - 19) = 0 x - 10 = 0 x - 13/9 = 0 x - 19 = 0 x = 10 x = 13/9 x = 19
Solve quickly: 8x = 0
8x = 0 8x = 0 x = 0 / 8 x = 0
Solve simultaneously: 9x + 9y = 9/5 3x + 1y = -17/5
9x + 9y = 9/5 3x + 1y = -17/5 Using elimination 3*(9x + 9y = 9/5) 9*(3x + 1y = -17/5) 27x + 27y = 27/5 27x + 9y = -153/5 Subtract equations 18y = 36 y = 36/18 y = 2 Substitute y 9x + 9(2) = 9/5 9x = -81/5 x = -81/5/9 x = -9/5
Solve the equations: 6x + 7y = -25/3 5x + 2y = -28/9
6x + 7y = -25/3 5x + 2y = -28/9 Using elimination 5*(6x + 7y = -25/3) 6*(5x + 2y = -28/9) 30x + 35y = -125/3 30x + 12y = -56/3 Subtract equations 23y = -23 y = -23/23 y = -1 Substitute y 6x + 7(-1) = -25/3 6x = -4/3 x = -4/3/6 x = -2/9
Find x in x^3 + 81/20x^2 + 141/40x - 7/8 = 0
x^3 + 81/20x^2 + 141/40x - 7/8 = 0 (x - 1/5)(x - -5/2)(x - -7/4) = 0 x - 1/5 = 0 x - -5/2 = 0 x - -7/4 = 0 x = 1/5 x = -5/2 x = -7/4
Find the solution to x^3 - 3/2x^2 - 35/2x + 18 = 0
x^3 - 3/2x^2 - 35/2x + 18 = 0 (x - 9/2)(x - -4)(x - 1) = 0 x - 9/2 = 0 x - -4 = 0 x - 1 = 0 x = 9/2 x = -4 x = 1
Find the solution to x^3 + 125/18x^2 - 175/6x + 125/9 = 0
x^3 + 125/18x^2 - 175/6x + 125/9 = 0 (x - 5/2)(x - -10)(x - 5/9) = 0 x - 5/2 = 0 x - -10 = 0 x - 5/9 = 0 x = 5/2 x = -10 x = 5/9
Find x in x^2 + 1x = 0
x^2 + 1x = 0 (x - -1)(x - 0) = 0 x - -1 = 0 or x - 0 = 0 x = -1 x = 0
Solve the equation x^3 + 5/2x^2 - 57/4x + 99/8 = 0
x^3 + 5/2x^2 - 57/4x + 99/8 = 0 (x - 3/2)(x - -11/2)(x - 3/2) = 0 x - 3/2 = 0 x - -11/2 = 0 x - 3/2 = 0 x = 3/2 x = -11/2 x = 3/2
Solve the equation x^2 - 6x + 5 = 0
x^2 - 6x + 5 = 0 (x - 1)(x - 5) = 0 x - 1 = 0 or x - 5 = 0 x = 1 x = 5
Find the solution to 6x - 12 = 0
6x - 12 = 0 6x = 12 x = 12 / 6 x = 2
Find x in x^2 + 1/42x - 1/42 = 0
x^2 + 1/42x - 1/42 = 0 (x - -1/6)(x - 1/7) = 0 x - -1/6 = 0 or x - 1/7 = 0 x = -1/6 x = 1/7
Solve quickly: x^2 + 3/2x - 1 = 0
x^2 + 3/2x - 1 = 0 (x - -2)(x - 1/2) = 0 x - -2 = 0 or x - 1/2 = 0 x = -2 x = 1/2
Determine x in 2x - 7 = 0
2x - 7 = 0 2x = 7 x = 7 / 2 x = 7/2
Find x and y such that 5x + 7y = -11/2 7x + 2y = 59/5
5x + 7y = -11/2 7x + 2y = 59/5 Using elimination 7*(5x + 7y = -11/2) 5*(7x + 2y = 59/5) 35x + 49y = -77/2 35x + 10y = 59 Subtract equations 39y = -195/2 y = -195/2/39 y = -5/2 Substitute y 5x + 7(-5/2) = -11/2 5x = 12 x = 12/5 x = 12/5
What value of x satisfies x^2 + 2x - 8 = 0
x^2 + 2x - 8 = 0 (x - 2)(x - -4) = 0 x - 2 = 0 or x - -4 = 0 x = 2 x = -4
Find the solution to 1x - 4/9 = 0
1x - 4/9 = 0 1x = 4/9 x = 4/9 / 1 x = 4/9
Solve the equation x^2 + 26/5x + 1 = 0
x^2 + 26/5x + 1 = 0 (x - -1/5)(x - -5) = 0 x - -1/5 = 0 or x - -5 = 0 x = -1/5 x = -5
Solve quickly: 1x + 10 = 0
1x + 10 = 0 1x = -10 x = -10 / 1 x = -10
Solve the system: 10x + 3y = 12 7x + 7y = 7/2
10x + 3y = 12 7x + 7y = 7/2 Using elimination 7*(10x + 3y = 12) 10*(7x + 7y = 7/2) 70x + 21y = 84 70x + 70y = 35 Subtract equations -49y = 49 y = 49/-49 y = -1 Substitute y 10x + 3(-1) = 12 10x = 15 x = 15/10 x = 3/2
Solve 10x - 75 = 0
10x - 75 = 0 10x = 75 x = 75 / 10 x = 15/2
Compute the solution of x^2 + 37/10x - 6/5 = 0
x^2 + 37/10x - 6/5 = 0 (x - -4)(x - 3/10) = 0 x - -4 = 0 or x - 3/10 = 0 x = -4 x = 3/10
Compute the solution of x^3 - 19/42x^2 - 193/21x + 80/7 = 0
x^3 - 19/42x^2 - 193/21x + 80/7 = 0 (x - 16/7)(x - -10/3)(x - 3/2) = 0 x - 16/7 = 0 x - -10/3 = 0 x - 3/2 = 0 x = 16/7 x = -10/3 x = 3/2
Find x in x^3 + 29/24x^2 - 221/48x = 0
x^3 + 29/24x^2 - 221/48x = 0 (x - 0)(x - -17/6)(x - 13/8) = 0 x - 0 = 0 x - -17/6 = 0 x - 13/8 = 0 x = 0 x = -17/6 x = 13/8
Solve the equation x^2 - 49/6x - 17/6 = 0
x^2 - 49/6x - 17/6 = 0 (x - 17/2)(x - -1/3) = 0 x - 17/2 = 0 or x - -1/3 = 0 x = 17/2 x = -1/3
Solve x^3 - 77/12x^2 + 4x + 17/12 = 0
x^3 - 77/12x^2 + 4x + 17/12 = 0 (x - 1)(x - -1/4)(x - 17/3) = 0 x - 1 = 0 x - -1/4 = 0 x - 17/3 = 0 x = 1 x = -1/4 x = 17/3
Solve simultaneously: 3x + 6y = -5 10x + 4y = -10/3
3x + 6y = -5 10x + 4y = -10/3 Using elimination 10*(3x + 6y = -5) 3*(10x + 4y = -10/3) 30x + 60y = -50 30x + 12y = -10 Subtract equations 48y = -40 y = -40/48 y = -5/6 Substitute y 3x + 6(-5/6) = -5 3x = 0 x = 0/3 x = 0
Compute the solution of x^3 - 4x^2 - 52x - 80 = 0
x^3 - 4x^2 - 52x - 80 = 0 (x - -2)(x - -4)(x - 10) = 0 x - -2 = 0 x - -4 = 0 x - 10 = 0 x = -2 x = -4 x = 10
Find x in 9x + 13 = 0
9x + 13 = 0 9x = -13 x = -13 / 9 x = -13/9
Determine x in x^3 + 53/9x^2 + 862/81x + 160/27 = 0
x^3 + 53/9x^2 + 862/81x + 160/27 = 0 (x - -3)(x - -16/9)(x - -10/9) = 0 x - -3 = 0 x - -16/9 = 0 x - -10/9 = 0 x = -3 x = -16/9 x = -10/9
Find x and y such that 2x + 4y = -46/9 7x + 5y = -233/9
2x + 4y = -46/9 7x + 5y = -233/9 Using elimination 7*(2x + 4y = -46/9) 2*(7x + 5y = -233/9) 14x + 28y = -322/9 14x + 10y = -466/9 Subtract equations 18y = 16 y = 16/18 y = 8/9 Substitute y 2x + 4(8/9) = -46/9 2x = -26/3 x = -26/3/2 x = -13/3
Find x in 10x - 180/7 = 0
10x - 180/7 = 0 10x = 180/7 x = 180/7 / 10 x = 18/7
Solve quickly: x^2 + 1/10x = 0
x^2 + 1/10x = 0 (x - 0)(x - -1/10) = 0 x - 0 = 0 or x - -1/10 = 0 x = 0 x = -1/10
Find x and y such that 5x + 1y = -13/6 5x + 9y = -23/2
5x + 1y = -13/6 5x + 9y = -23/2 Using elimination 5*(5x + 1y = -13/6) 5*(5x + 9y = -23/2) 25x + 5y = -65/6 25x + 45y = -115/2 Subtract equations -40y = 140/3 y = 140/3/-40 y = -7/6 Substitute y 5x + 1(-7/6) = -13/6 5x = -1 x = -1/5 x = -1/5
Determine x in x^2 - 115/6x + 221/6 = 0
x^2 - 115/6x + 221/6 = 0 (x - 17)(x - 13/6) = 0 x - 17 = 0 or x - 13/6 = 0 x = 17 x = 13/6
Find the solution to x^3 - 31/20x^2 - 6/5x + 27/20 = 0
x^3 - 31/20x^2 - 6/5x + 27/20 = 0 (x - 3/4)(x - 9/5)(x - -1) = 0 x - 3/4 = 0 x - 9/5 = 0 x - -1 = 0 x = 3/4 x = 9/5 x = -1
Solve x^2 + 22/5x + 63/20 = 0
x^2 + 22/5x + 63/20 = 0 (x - -9/10)(x - -7/2) = 0 x - -9/10 = 0 or x - -7/2 = 0 x = -9/10 x = -7/2
Find x in x^2 + 3x + 182/81 = 0
x^2 + 3x + 182/81 = 0 (x - -13/9)(x - -14/9) = 0 x - -13/9 = 0 or x - -14/9 = 0 x = -13/9 x = -14/9
Solve quickly: x^3 - 287/60x^2 + 97/24x - 5/8 = 0
x^3 - 287/60x^2 + 97/24x - 5/8 = 0 (x - 15/4)(x - 5/6)(x - 1/5) = 0 x - 15/4 = 0 x - 5/6 = 0 x - 1/5 = 0 x = 15/4 x = 5/6 x = 1/5
Find the solution to x^3 - 115/36x^2 + 73/36x + 13/18 = 0
x^3 - 115/36x^2 + 73/36x + 13/18 = 0 (x - 13/9)(x - 2)(x - -1/4) = 0 x - 13/9 = 0 x - 2 = 0 x - -1/4 = 0 x = 13/9 x = 2 x = -1/4
Compute the solution of x^3 + 51/4x^2 + 159/8x + 55/8 = 0
x^3 + 51/4x^2 + 159/8x + 55/8 = 0 (x - -1/2)(x - -5/4)(x - -11) = 0 x - -1/2 = 0 x - -5/4 = 0 x - -11 = 0 x = -1/2 x = -5/4 x = -11
Solve quickly: 10x - 20 = 0
10x - 20 = 0 10x = 20 x = 20 / 10 x = 2
Solve the equations: 8x + 10y = 662/9 1x + 7y = 445/9
8x + 10y = 662/9 1x + 7y = 445/9 Using elimination 1*(8x + 10y = 662/9) 8*(1x + 7y = 445/9) 8x + 10y = 662/9 8x + 56y = 3560/9 Subtract equations -46y = -322 y = -322/-46 y = 7 Substitute y 8x + 10(7) = 662/9 8x = 32/9 x = 32/9/8 x = 4/9
Find x for 2x - 10/3 = 0
2x - 10/3 = 0 2x = 10/3 x = 10/3 / 2 x = 5/3
Find x in x^3 - 53/6x^2 - 109/3x - 20 = 0
x^3 - 53/6x^2 - 109/3x - 20 = 0 (x - 12)(x - -2/3)(x - -5/2) = 0 x - 12 = 0 x - -2/3 = 0 x - -5/2 = 0 x = 12 x = -2/3 x = -5/2
Solve the equations: 2x + 8y = 482/63 1x + 8y = 349/63
2x + 8y = 482/63 1x + 8y = 349/63 Using elimination 1*(2x + 8y = 482/63) 2*(1x + 8y = 349/63) 2x + 8y = 482/63 2x + 16y = 698/63 Subtract equations -8y = -24/7 y = -24/7/-8 y = 3/7 Substitute y 2x + 8(3/7) = 482/63 2x = 38/9 x = 38/9/2 x = 19/9
Solve the equations: 3x + 6y = 156/5 3x + 5y = 131/5
3x + 6y = 156/5 3x + 5y = 131/5 Using elimination 3*(3x + 6y = 156/5) 3*(3x + 5y = 131/5) 9x + 18y = 468/5 9x + 15y = 393/5 Subtract equations 3y = 15 y = 15/3 y = 5 Substitute y 3x + 6(5) = 156/5 3x = 6/5 x = 6/5/3 x = 2/5
Determine x in x^2 + 45/7x + 68/7 = 0
x^2 + 45/7x + 68/7 = 0 (x - -4)(x - -17/7) = 0 x - -4 = 0 or x - -17/7 = 0 x = -4 x = -17/7
What value of x satisfies 9x + 117/8 = 0
9x + 117/8 = 0 9x = -117/8 x = -117/8 / 9 x = -13/8
Determine x in x^3 - 97/15x^2 + 56/5x - 16/3 = 0
x^3 - 97/15x^2 + 56/5x - 16/3 = 0 (x - 5/3)(x - 4/5)(x - 4) = 0 x - 5/3 = 0 x - 4/5 = 0 x - 4 = 0 x = 5/3 x = 4/5 x = 4
Solve quickly: x^3 + 61/45x^2 - 61/45x - 1 = 0
x^3 + 61/45x^2 - 61/45x - 1 = 0 (x - -5/9)(x - -9/5)(x - 1) = 0 x - -5/9 = 0 x - -9/5 = 0 x - 1 = 0 x = -5/9 x = -9/5 x = 1
Solve simultaneously: 4x + 1y = 67/9 5x + 10y = 1265/9
4x + 1y = 67/9 5x + 10y = 1265/9 Using elimination 5*(4x + 1y = 67/9) 4*(5x + 10y = 1265/9) 20x + 5y = 335/9 20x + 40y = 5060/9 Subtract equations -35y = -525 y = -525/-35 y = 15 Substitute y 4x + 1(15) = 67/9 4x = -68/9 x = -68/9/4 x = -17/9
Solve the equation x^2 + 3/2x - 27 = 0
x^2 + 3/2x - 27 = 0 (x - 9/2)(x - -6) = 0 x - 9/2 = 0 or x - -6 = 0 x = 9/2 x = -6
Compute the solution of x^2 + 17/2x - 15 = 0
x^2 + 17/2x - 15 = 0 (x - -10)(x - 3/2) = 0 x - -10 = 0 or x - 3/2 = 0 x = -10 x = 3/2
Find the solution to 7x - 7 = 0
7x - 7 = 0 7x = 7 x = 7 / 7 x = 1
Solve the equations: 8x + 10y = 34 4x + 2y = 67/5
8x + 10y = 34 4x + 2y = 67/5 Using elimination 4*(8x + 10y = 34) 8*(4x + 2y = 67/5) 32x + 40y = 136 32x + 16y = 536/5 Subtract equations 24y = 144/5 y = 144/5/24 y = 6/5 Substitute y 8x + 10(6/5) = 34 8x = 22 x = 22/8 x = 11/4