Question

Solve the system of equations. −6x+2y=−32
4x+3y=−9

Answer 1

To solve the system of equations, we can use the method of substitution or elimination.

Method 1: Substitution

From the first equation, we can solve for x in terms of y:
-6x + 2y = -32
-6x = -2y - 32
x = (2y + 32)/6
x = (y + 16)/3

Substitute this expression for x into the second equation:
4x + 3y = -9
4((y + 16)/3) + 3y = -9
(4/3)(y + 16) + 3y = -9
(4/3)y + (64/3) + 3y = -9
(13/3)y + (64/3) = -9
(13/3)y = -73/3
y = (-73/3)(3/13)
y = -73/13

Substitute this value of y back into the expression for x:
x = (y + 16)/3
x = (-73/13 + 16)/3
x = (-73 + 208)/39
x = 135/39
x = 45/13

So the solution to the system of equations is x = 45/13 and y = -73/13.

Method 2: Elimination

Multiply the first equation by 2 and the second equation by -3 to get the coefficients of x to cancel out:
-12x + 4y = -64
-12x - 9y = 27

Combine the two equations:
(-12x + 4y) - (-12x - 9y) = -64 - 27
-12x + 4y + 12x + 9y = -91
13y = -91
y = -91/13
y = -7

Substitute this value of y back into one of the original equations:
-6x + 2y = -32
-6x + 2(-7) = -32
-6x - 14 = -32
-6x = -18
x = (-18)/(-6)
x = 3

So the solution to the system of equations is x = 3 and y = -7.