To solve the system:
[tex]\begin{gathered} 2x-6y=-12 \\ x+2y=14 \end{gathered}[/tex]we mutiply the second equation by two, then:
[tex]\begin{gathered} 2x-6y=-12 \\ 2x+4y=28 \end{gathered}[/tex]Now we substract the second equation from the first one:
[tex]\begin{gathered} -10y=-40 \\ y=\frac{-40}{-10} \\ y=4 \end{gathered}[/tex]Once we have the valu of y we plug it in the second equation and solve for x:
[tex]\begin{gathered} x+2(4)=14 \\ x=14-8 \\ x=6 \end{gathered}[/tex]Therefore, x=6 and y=4.
