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 will use the elimination method.
First, let's rearrange Equation 2 to express \(y\) in terms of \(x\):
\[ y = 6x + 32 \] (Equation 3)
Now, we can substitute Equation 3 into Equation 1:
\[ 4x - 8(6x + 32) = -36 \]
Expanding that gives:
\[ 4x - 48x - 256 = -36 \]
Combining the \(x\) terms:
\[ -44x - 256 = -36 \]
Next, we will 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 Equation 3 to find \(y\):
\[ y = 6(-5) + 32 \] \[ y = -30 + 32 \] \[ y = 2 \]
Thus, the solution to the system of equations is:
\((x, y) = (-5, 2)\)
So, the answer is: \[ (-5, 2) \]