To solve the system of equations:
- \(4x - 8y = -36\) (Equation 1)
- \(-6x + y = 32\) (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:
\[ \boxed{(-5, 2)} \]