To solve the system of equations:
- \( 5x - 4y = -44 \) (Equation 1)
- \( -x + 3y = 22 \) (Equation 2)
Let's solve this system using the substitution or elimination method. Here, we'll use substitution.
First, we can solve Equation 2 for \( x \):
\[ -x + 3y = 22 \] \[ -x = 22 - 3y \] \[ x = 3y - 22 \]
Now we can substitute \( x \) in Equation 1:
\[ 5(3y - 22) - 4y = -44 \]
Distributing the \( 5 \):
\[ 15y - 110 - 4y = -44 \]
Combining like terms:
\[ 11y - 110 = -44 \]
Adding \( 110 \) to both sides:
\[ 11y = 66 \]
Dividing by \( 11 \):
\[ y = 6 \]
Now that we have the value for \( y \), we can substitute it back to find \( x \):
\[ x = 3(6) - 22 \] \[ x = 18 - 22 \] \[ x = -4 \]
Thus, the solution to the system of equations is:
\[ \boxed{(x, y) = (-4, 6)} \]
To verify, we can check both equations:
- For Equation 1: \( 5(-4) - 4(6) = -20 - 24 = -44 \) (True)
- For Equation 2: \( -(-4) + 3(6) = 4 + 18 = 22 \) (True)
Both equations are satisfied, confirming that the solution is correct.