Question

solve the system of equations.
4x - 8y = -36
-6x + y = 32

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, we'll use the substitution method.

First, let's solve Equation 2 for \(y\):

\[
y = 6x + 32
\]

Now, we can substitute this expression for \(y\) into Equation 1:

\[
4x - 8(6x + 32) = -36
\]

Distribute \(-8\):

\[
4x - 48x - 256 = -36
\]

Combine like terms:

\[
-44x - 256 = -36
\]

Now, add 256 to both sides:

\[
-44x = -36 + 256
\]

\[
-44x = 220
\]

Divide by \(-44\):

\[
x = \frac{220}{-44} = -5
\]

Now that we have \(x\), substitute it back into the expression we found for \(y\):

\[
y = 6(-5) + 32
\]

\[
y = -30 + 32
\]

\[
y = 2
\]

Thus, the solution to the system of equations is:

\[
\boxed{(-5, 2)}
\]