To solve the given system of equations:
- \(-6x + 2y = -32\)
- \(4x + 3y = -9\)
Let's start by manipulating the first equation to solve for \(y\):
Step 1: Solve for \(y\) in the first equation.
The first equation can be rewritten for \(y\):
\[ -6x + 2y = -32 \]
Add \(6x\) to both sides:
\[ 2y = 6x - 32 \]
Now, divide by 2:
\[ y = 3x - 16 \]
Step 2: Substitute \(y\) into the second equation.
Now substitute \(y\) in the second equation:
\[ 4x + 3(3x - 16) = -9 \]
Distribute \(3\):
\[ 4x + 9x - 48 = -9 \]
Combine like terms:
\[ 13x - 48 = -9 \]
Step 3: Solve for \(x\).
Add \(48\) to both sides:
\[ 13x = 39 \]
Now divide by \(13\):
\[ x = 3 \]
Step 4: Find \(y\) using \(x = 3\).
Now we substitute \(x = 3\) back into \(y = 3x - 16\):
\[ y = 3(3) - 16 \] \[ y = 9 - 16 \] \[ y = -7 \]
Final Solution
Thus, the solution to the system of equations is:
\[ (x, y) = (3, -7) \]
So the answer is \((3, -7)\).