To solve the system of equations:
- Equation 1: \(-6x + 2y = -32\)
- Equation 2: \(4x + 3y = -9\)
We can use the substitution or elimination method. Here, I'll use the elimination method.
First, let's rewrite the first equation in a simpler form. Divide the entire equation by 2:
\[ -3x + y = -16 \quad \text{(Equation 1 simplified)} \]
Now we have:
- \( -3x + y = -16 \)
- \( 4x + 3y = -9 \)
Next, we can express \(y\) from the first equation:
\[ y = 3x - 16 \]
Now substitute this expression for \(y\) into the second equation:
\[ 4x + 3(3x - 16) = -9 \]
Distributing:
\[ 4x + 9x - 48 = -9 \]
Combine like terms:
\[ 13x - 48 = -9 \]
Add 48 to both sides:
\[ 13x = 39 \]
Now, divide by 13:
\[ x = 3 \]
Now that we have \(x\), we can substitute it back into the equation for \(y\):
\[ y = 3(3) - 16 \] \[ y = 9 - 16 \] \[ y = -7 \]
Thus, the solution to the system of equations is:
\[ (x, y) = (3, -7) \]
So the answer is \((3, -7)\).