Let's rewrite the system as:
[tex]\begin{cases}x+2y=7_{\text{ }}{(1)} \\ 3x-y={-2_{\text{ }}}(2)\end{cases}[/tex]Using elimination:
[tex]\begin{gathered} (1)+2(2) \\ x+6x+2y-2y=7-4 \\ 7x=3 \\ x=\frac{3}{7} \end{gathered}[/tex]Replace x into (2):
[tex]\begin{gathered} y=3(\frac{3}{7})+2 \\ y=\frac{23}{7} \end{gathered}[/tex]