To solve the system of equations:
- \( 4x - 2y = -2 \)
- \( -3x + 5y = -9 \)
We can use the method of substitution or elimination. Here, I'll use the elimination method.
First, let's rearrange the first equation to express \( y \) in terms of \( x \):
\[ 4x - 2y = -2 \] Adding \( 2y \) to both sides: \[ 4x = 2y - 2 \] Now, let's isolate \( y \): \[ 2y = 4x + 2 \] Divide by 2: \[ y = 2x + 1 \]
Now, we substitute \( y = 2x + 1 \) into the second equation:
\[ -3x + 5(2x + 1) = -9 \]
Distributing \( 5 \): \[ -3x + 10x + 5 = -9 \] Combine like terms: \[ 7x + 5 = -9 \] Subtracting \( 5 \) from both sides: \[ 7x = -14 \] Dividing by \( 7 \): \[ x = -2 \]
Now we substitute \( x = -2 \) back into the expression for \( y \): \[ y = 2(-2) + 1 \] \[ y = -4 + 1 \] \[ y = -3 \]
Thus, the solution to the system of equations is: \[ (x, y) = (-2, -3) \]
To summarize:
The solution is \( x = -2 \) and \( y = -3 \).