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 elimination method.
First, let's rewrite Equation 2 to express \( x \) in terms of \( y \): \[ -x + 3y = 22 \] Add \( x \) to both sides: \[ 3y = x + 22 \quad \Rightarrow \quad x = 3y - 22 \quad \text{(Equation 3)} \]
Now, substitute Equation 3 into Equation 1: \[ 5(3y - 22) - 4y = -44 \] Distribute the 5: \[ 15y - 110 - 4y = -44 \] Combine like terms: \[ 15y - 4y - 110 = -44 \] \[ 11y - 110 = -44 \] Add 110 to both sides: \[ 11y = 66 \] Divide by 11: \[ y = 6 \]
Now 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: \[ (x, y) = (-4, 6) \]
Final Answer: \[ (-4, 6) \]