To solve the system of equations:
- \( 5x - 4y = -44 \) (Equation 1)
- \( -x + 3y = 22 \) (Equation 2)
We'll start by solving Equation 2 for \( x \):
\[ -x + 3y = 22 \] \[ x = 3y - 22 \]
Now, substitute \( x \) in Equation 1:
\[ 5(3y - 22) - 4y = -44 \]
Distribute \( 5 \):
\[ 15y - 110 - 4y = -44 \]
Combine like terms:
\[ 11y - 110 = -44 \]
Add \( 110 \) to both sides:
\[ 11y = 66 \]
Now, divide by \( 11 \):
\[ y = 6 \]
Now that we have \( y \), substitute it back into the equation we found for \( x \):
\[ x = 3(6) - 22 \] \[ x = 18 - 22 \] \[ x = -4 \]
Thus, the solution to the system of equations is:
\[ (x, y) = (-4, 6) \]
Final answer:
\[ (-4, 6) \]