Answer
See below
Work Step by Step
Given: $7x-12y=-22\\25x+8y=14$
Multiply both sides of the first equation by $2$:
$14x-24y=-44$
Multiply both sides of the second equation by $3$:
$75x+24y=52$
Add the new first equation:
$89x=-2\\
\rightarrow x=-\frac{2}{89}$
Find y: $7(-\frac{2}{89})-12y=-22\\
\rightarrow y=\frac{162}{89}$