To solve the system of equations:
- \(-6x + 2y = -32\)
- \(4x + 3y = -9\)
Let's first simplify the first equation. We can divide the entire equation by 2:
\[ -3x + y = -16 \]
Now we can rewrite it in terms of \(y\):
\[ y = 3x - 16 \quad \text{(Equation 1)} \]
Next, we can substitute this expression for \(y\) into the second equation:
\[ 4x + 3(3x - 16) = -9 \]
Now, simplify the equation:
\[ 4x + 9x - 48 = -9 \] \[ 13x - 48 = -9 \]
Adding 48 to both sides:
\[ 13x = 39 \]
Now, divide by 13:
\[ x = 3 \]
Now that we have \(x\), we can substitute it back into Equation 1 to find \(y\):
\[ y = 3(3) - 16 \] \[ y = 9 - 16 \] \[ y = -7 \]
Thus, the solution to the system of equations is:
\[ \boxed{(3, -7)} \]