Let:
[tex]\begin{gathered} 2y=x+6_{\text{ }}(1) \\ 3x=y+7_{\text{ }}(2) \end{gathered}[/tex]From (1) solve for y:
[tex]y=\frac{x+6}{2}_{\text{ }}(3)[/tex]Replace (3) into (2):
[tex]3x=\frac{x+6}{2}+7[/tex]Solve for x:
[tex]\begin{gathered} 6x=x+6+14 \\ 6x-x=20 \\ 5x=20 \\ x=\frac{20}{5} \\ x=4 \end{gathered}[/tex]Replace x into (3):
[tex]\begin{gathered} y=\frac{4+6}{2} \\ y=\frac{10}{2} \\ y=5 \end{gathered}[/tex]Answer:
x = 4
y = 5
or
(4,5)
