Question

Solve the system of equations using any method.
4x−8y=−36

−6x+y=32


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Answer 1

To solve the system of equations:

1. \( 4x - 8y = -36 \) (Equation 1)
2. \( -6x + y = 32 \) (Equation 2)

We can use the substitution or elimination method. Here, I'll use the substitution method by first solving Equation 2 for \( y \):

From Equation 2:
\[
y = 6x + 32
\]

Next, substitute \( y \) in Equation 1 with \( 6x + 32 \):
\[
4x - 8(6x + 32) = -36
\]

Now, distribute the \(-8\):
\[
4x - 48x - 256 = -36
\]

Combine like terms:
\[
-44x - 256 = -36
\]

Now, isolate \( x \):
\[
-44x = -36 + 256
\]
\[
-44x = 220
\]
\[
x = \frac{220}{-44} = -5
\]

Now substitute \( x = -5 \) back into the equation \( y = 6x + 32 \) to find \( y \):
\[
y = 6(-5) + 32
\]
\[
y = -30 + 32
\]
\[
y = 2
\]

So the solution to the system of equations is:
\[
(x, y) = (-5, 2)
\]

Thus, the answer is:
\[
\boxed{(-5, 2)}
\]