Solve the system of equations.

Question

−6x+2y=−32
4x+3y=−9 (1 point)
(
,
)

Answer 1

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

Let's use the method of substitution:

1) Solve the first equation for x in terms of y:
-6x + 2y = -32
-6x = -2y - 32
x = (2y + 32)/-6
x = (-y/3) - (16/3) (equation 2)

2) Substitute the expression for x in the second equation:
4x + 3y = -9
4((-y/3) - (16/3)) + 3y = -9
(-4y/3) - (64/3) + 3y = -9
Multiply through by 3 to remove the fraction:
-4y - 64 + 9y = -27
5y - 64 = -27
5y = 37
y = 37/5

3) Substitute the value of y back into equation 2 to solve for x:
x = (-y/3) - (16/3)
x = (-(37/5)/3) - (16/3)
x = (-37/5)*(1/3) - (16/3)
x = -37/15 - 16/3
x = (-37/15) - (16/3)
x = (-37/15) - (80/15)
x = -117/15
x = -39/5

Therefore, the solution to the system of equations is (x, y) = (-39/5, 37/5).