Subtract the corresponding sides of one equation from the other:
\(\begin{cases}-2x-2y=-6\\x-2y=15\end{cases}\)
\(\implies (-2x-2y)-(x-2y)=-6-15\)
\(\implies -3x+0y=-21\)
\(\implies x=7\)
Now plug this into either equation to find \(y\).
\(x-2y=15\implies 7-2y=15\)
\(\implies-2y=8\)
\(\implies y=-4\)
