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.
Step 1: Solve Equation 2 for \( y \)
From Equation 2, we can express \( y \) in terms of \( x \):
\[ y = 6x + 32 \]
Step 2: Substitute \( y \) into Equation 1
Now substitute this expression for \( y \) into Equation 1:
\[ 4x - 8(6x + 32) = -36 \]
Step 3: Simplify the equation
Distributing \( -8 \):
\[ 4x - 48x - 256 = -36 \]
Combine like terms:
\[ -44x - 256 = -36 \]
Step 4: Solve for \( x \)
Add 256 to both sides:
\[ -44x = -36 + 256 \] \[ -44x = 220 \]
Now divide by -44:
\[ x = \frac{220}{-44} = -5 \]
Step 5: Substitute \( x \) back to find \( y \)
Now substitute \( x = -5 \) back into the equation for \( y \):
\[ y = 6(-5) + 32 \] \[ y = -30 + 32 \] \[ y = 2 \]
Step 6: Solution
The solution to the system of equations is:
\[ (x, y) = (-5, 2) \]
So the final answer is:
\[ (-5, 2) \]