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, I will use the substitution method.
First, we can solve Equation 2 for \(x\):
\[ -x + 3y = 22 \implies x = 3y - 22 \]
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 substitute \(y\) back to find \(x\):
\[ x = 3(6) - 22 \] \[ x = 18 - 22 \] \[ x = -4 \]
Thus, the solution to the system of equations is:
\[ (x, y) = (-4, 6) \]
The final answer is:
\[ (-4, 6) \]