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