Let:
[tex]\begin{gathered} 3x+y=-3\text{ (1)} \\ -2x+y=7\text{ (2)} \end{gathered}[/tex]From (1) solve for y:
[tex]y=-3-3x\text{ (3)}[/tex]Replace (3) into (2):
[tex]\begin{gathered} -2x+(-3-3x)=7 \\ -2x-3-3x=7 \\ -5x-3=7 \\ -5x=10 \\ x=\frac{10}{-5} \\ x=-2 \end{gathered}[/tex]Replace x into (3):
[tex]\begin{gathered} y=-3-3(-2) \\ y=-3+6 \\ y=3 \end{gathered}[/tex]