To solve the system of equations:
- \( 4x - 8y = -36 \)
- \( -6x + y = 32 \)
we can use either the substitution method, the elimination method, or graph the equations. Here, I will use the elimination method.
First, let's rearrange the second equation to express \( y \) in terms of \( x \):
\[ y = 6x + 32 \]
Now we can substitute this expression for \( y \) into the first equation:
\[ 4x - 8(6x + 32) = -36 \]
Distributing the \(-8\):
\[ 4x - 48x - 256 = -36 \]
Combine like terms:
\[ -44x - 256 = -36 \]
Add \( 256 \) to both sides:
\[ -44x = 220 \]
Now, divide by \(-44\):
\[ x = -5 \]
Now, substitute \( x = -5 \) back into the equation for \( y \):
\[ y = 6(-5) + 32 \] \[ y = -30 + 32 \] \[ y = 2 \]
Thus, the solution to the system of equations is:
\[ \boxed{(-5, 2)} \]