[tex]5x+3y=-12 \ \ \ |\times (- 7) \\
8x+7y=-6 \ \ \ | \times 3\\ \\
-35x-21y=84 \\
\underline{24x+21y=-18 \ } \\
-35x+24x=84-18 \\
-11x=66 \ \ \ |\div (-11) \\
x=-6 \\ \\
5x+3y=-12 \\
5 \times (-6)+3y=-12 \\
-30+3y=-12 \ \ \ |+30 \\
3y=18 \ \ \ |\div 3 \\
y=6 \\ \\
\boxed{(x,y)=(-6,6)}
[/tex]