To solve the system of equations:
- \(-6x + 2y = -32\)
- \(4x + 3y = -9\)
We can use either the substitution method or the elimination method. Here, we'll use the elimination method.
First, we can simplify the first equation. Divide the entire equation by 2:
\[ -3x + y = -16 \]
Now we can rewrite the system of equations:
- \(-3x + y = -16\)
- \(4x + 3y = -9\)
Next, we can express \(y\) from the first equation:
\[ y = 3x - 16 \]
Now, substitute \(y\) in the second equation:
\[ 4x + 3(3x - 16) = -9 \]
Distributing:
\[ 4x + 9x - 48 = -9 \]
Combine like terms:
\[ 13x - 48 = -9 \]
Add 48 to both sides:
\[ 13x = 39 \]
Divide by 13:
\[ x = 3 \]
Now, substitute \(x = 3\) back into the equation for \(y\):
\[ y = 3(3) - 16 \] \[ y = 9 - 16 \] \[ y = -7 \]
So, the solution to the system of equations is:
\[ \boxed{(3, -7)} \]