To solve the system of equations, we can use the method of substitution or elimination. Let's use the elimination method for this problem.
The given equations are:
- \( 5x - 4y = -44 \)
- \( -x + 3y = 22 \)
Let's first manipulate the second equation to express \( x \) in terms of \( y \):
From the second equation: \[ -x + 3y = 22 \] Adding \( x \) to both sides gives: \[ 3y = x + 22 \] Now, we can solve for \( x \): \[ x = 3y - 22 \]
Next, we substitute \( x \) in the first equation with \( 3y - 22 \): \[ 5(3y - 22) - 4y = -44 \] Distributing \( 5 \) gives: \[ 15y - 110 - 4y = -44 \] Combining like terms: \[ 15y - 4y - 110 = -44 \] \[ 11y - 110 = -44 \] Now add \( 110 \) to both sides: \[ 11y = 66 \] Now divide by \( 11 \): \[ y = 6 \]
Now that we have \( y \), we can find \( x \) using the expression \( x = 3y - 22 \): \[ x = 3(6) - 22 \] \[ x = 18 - 22 \] \[ x = -4 \]
Thus, the solution to the system of equations is: \[ (x, y) = (-4, 6) \]
So the final answer is: \[ \boxed{(-4, 6)} \]
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