To solve the system of equations:
- \( 4x - 8y = -36 \) (Equation 1)
- \( -6x + y = 32 \) (Equation 2)
We can use either substitution or elimination methods. Here, we'll use the substitution method.
First, let's solve Equation 2 for \( y \):
\[ y = 6x + 32 \]
Next, we can substitute this expression for \( y \) into Equation 1:
\[ 4x - 8(6x + 32) = -36 \]
Now, distribute the \( -8 \) across the terms in the parentheses:
\[ 4x - 48x - 256 = -36 \]
Combine like terms:
\[ -44x - 256 = -36 \]
Next, add 256 to both sides:
\[ -44x = 220 \]
Now, divide both sides by -44:
\[ x = \frac{220}{-44} = -5 \]
Now that we have \( x \), we can substitute it back into the equation for \( y \):
\[ y = 6(-5) + 32 \] \[ y = -30 + 32 \] \[ y = 2 \]
Thus, the solution to the system of equations is:
\[ (x, y) = (-5, 2) \]
The answer is \( (-5, 2) \).