To solve the given system, first, let's multiply the second equation by 3
[tex]\begin{gathered} 3x+4y=24 \\ -3x+6y=6 \end{gathered}[/tex]Then, we combine the equations
[tex]\begin{gathered} 3x-3x+4y+6y=24+6 \\ 10y=30 \\ y=\frac{30}{10} \\ y=3 \end{gathered}[/tex]Now, we find x
[tex]\begin{gathered} -x+2y=2 \\ -x+2\cdot3=2 \\ -x+6=2 \\ -x=2-6 \\ -x=-4 \\ x=4 \end{gathered}[/tex]