To solve the system of equations:
- \( 4x - 8y = -36 \) --- (Equation 1)
- \( -6x + y = 32 \) --- (Equation 2)
We'll use the substitution or elimination method. Let's start with Equation 2 and solve for \( y \):
\[ y = 6x + 32 \]
Now we can substitute \( y \) in Equation 1:
\[ 4x - 8(6x + 32) = -36 \]
Now let's simplify this:
\[ 4x - 48x - 256 = -36 \]
Combine the \( x \) terms:
\[ -44x - 256 = -36 \]
Now add 256 to both sides:
\[ -44x = 220 \]
Now divide 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:
\[ \boxed{(-5, 2)} \]