12) \( \begin{aligned} x-8 y & =-22 \\ -x+7 y & =19\end{aligned} \)

To solve the system of equations: 1) \( x - 8y = -22 \) 2) \( -x + 7y = 19 \) We can solve for \( x \) from the first equation: \[ x = 8y - 22 \] Next, we can substitute \( x \) in the second equation: \[-(8y - 22) + 7y = 19 \] This simplifies to: \[-8y + 22 + 7y = 19\] \[-y + 22 = 19\] \[-y = 19 - 22\] \[-y = -3\] \[y = 3\] Now substitute \( y = 3 \) back into the first equation to find \( x \): \[ x - 8(3) = -22 \] \[ x - 24 = -22 \] \[ x = -22 + 24 \] \[ x = 2 \] Thus, the solution to the system of equations is: \( x = 2 \) and \( y = 3 \). Final answer: \( (x, y) = (2, 3) \)