To solve the system of equations:
- \( 5x - 4y = -44 \) (Equation 1)
- \( -x + 3y = 22 \) (Equation 2)
We can use the substitution or elimination method. Here, we'll use the elimination method.
First, let's rearrange Equation 2 to express \( x \) in terms of \( y \):
\[ -x + 3y = 22 \] Adding \( x \) to both sides gives: \[ 3y = x + 22 \] So we have: \[ x = 3y - 22 \quad \text{(Equation 3)} \]
Now substitute Equation 3 into Equation 1:
\[ 5(3y - 22) - 4y = -44 \] Distributing the \( 5 \): \[ 15y - 110 - 4y = -44 \] Combine the \( y \) terms: \[ 15y - 4y = 11y \] So we have: \[ 11y - 110 = -44 \] Now add \( 110 \) to both sides: \[ 11y = 110 - 44 \] \[ 11y = 66 \] To solve for \( y \), divide by \( 11 \): \[ y = 6 \]
Now substitute \( y \) back into Equation 3 to find \( x \): \[ x = 3(6) - 22 \] \[ x = 18 - 22 \] \[ x = -4 \]
The solution to the system of equations is: \[ (x, y) = (-4, 6) \]
Thus, the final answer is: \[ \boxed{(-4, 6)} \]