Let:
[tex]\begin{gathered} 7x-y=10_{\text{ }}(1) \\ -5x+y=12_{\text{ }}(2) \end{gathered}[/tex]Using elimination method:
[tex]\begin{gathered} (1)+(2) \\ 7x-5x-y+y=10+12 \\ 2x=22 \\ x=\frac{22}{2} \\ x=11 \end{gathered}[/tex]Replace the value of x into (2):
[tex]\begin{gathered} -5(11)+y=12 \\ -55+y=12 \\ y=12+55 \\ y=67 \end{gathered}[/tex]