To solve the system of equations:
- \( 5x - 4y = -44 \) (Equation 1)
- \( -x + 3y = 22 \) (Equation 2)
We can use the substitution method or the elimination method. Here, we will use the substitution method.
First, let's solve Equation 2 for \( x \):
\[ -x + 3y = 22 \]
Adding \( x \) to both sides:
\[ 3y = x + 22 \]
Now, isolate \( x \):
\[ x = 3y - 22 \quad (3) \]
Next, substitute \( x \) from Equation (3) 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:
\[ 11y = 66 \]
And then divide by 11:
\[ y = 6 \]
Now that we have \( y \), we substitute \( y = 6 \) back into Equation (3) to find \( x \):
\[ x = 3(6) - 22 \] \[ x = 18 - 22 \] \[ x = -4 \]
Thus, the solution to the system of equations is:
\[ (x, y) = (-4, 6) \]
To check our solution, let's plug \( x = -4 \) and \( y = 6 \) back into the original equations:
-
For the first equation: \[ 5(-4) - 4(6) = -20 - 24 = -44 \quad \text{(correct)} \]
-
For the second equation: \[ -(-4) + 3(6) = 4 + 18 = 22 \quad \text{(correct)} \]
Both equations are satisfied. Therefore, the final answer is:
\[ \boxed{(-4, 6)} \]