To solve the system of equations:
- \( 5x - 4y = -44 \) (Equation 1)
- \( -x + 3y = 22 \) (Equation 2)
Let's solve this step by step.
First, we can solve Equation 2 for \( x \):
\[ -x + 3y = 22 \implies x = 3y - 22 \]
Now, substitute this expression for \( x \) into Equation 1:
\[ 5(3y - 22) - 4y = -44 \]
Expanding this gives:
\[ 15y - 110 - 4y = -44 \]
Combine like terms:
\[ 11y - 110 = -44 \]
Now, add 110 to both sides:
\[ 11y = 66 \]
Next, divide by 11:
\[ y = 6 \]
Now that we have \( y \), substitute \( y = 6 \) back into the equation for \( x \):
\[ x = 3(6) - 22 \] \[ x = 18 - 22 \] \[ x = -4 \]
Thus, the solution to the system of equations is:
\[ (x, y) = (-4, 6) \]
Therefore, the answer is:
\[ (-4, 6) \]