To solve the system of equations given by:
- \( 4x - 8y = -36 \) (Equation 1)
- \( -6x + y = 32 \) (Equation 2)
Let's start by rewriting both equations.
Step 1: Isolate \( y \) in Equation 2.
From Equation 2: \[ y = 6x + 32 \]
Step 2: Substitute \( y \) in Equation 1.
Now, substitute \( y \) from Equation 2 into Equation 1: \[ 4x - 8(6x + 32) = -36 \]
Step 3: Simplify the equation. \[ 4x - 48x - 256 = -36 \] \[ -44x - 256 = -36 \]
Step 4: Solve for \( x \). Add 256 to both sides: \[ -44x = 220 \]
Now divide by -44: \[ x = -\frac{220}{44} = -5 \]
Step 5: Substitute \( x \) back to find \( y \).
Using Equation 2: \[ y = 6(-5) + 32 \] \[ y = -30 + 32 = 2 \]
Final Solution:
The solution to the system of equations is: \[ (x, y) = (-5, 2) \]
Thus, the final answer is: \[ \boxed{(-5, 2)} \]