We want to find the solutions for the following system
[tex]\begin{cases}-12x+y=-18 \\ -6x-3y=12\end{cases}[/tex]We can start simplifying, by dividing all terms in the second equation by 3
[tex]\begin{cases}-12x+y=-18 \\ -2x-y=4\end{cases}[/tex]Now, we can add those equations together and get a new one only for x
[tex]\begin{gathered} -12x+y+(-2x-y)=-18+(4) \\ -14x=-14 \\ x=1 \end{gathered}[/tex]Now that we have the solution for x, we can substitute its value in any of the equations to get the value for y.
[tex]\begin{cases}x=1 \\ -2x-y=4\end{cases}\Rightarrow-2\cdot(1)-y=4\Rightarrow y=-6[/tex]And those are our solutions.
[tex]\begin{cases}x=1 \\ y=-6\end{cases}[/tex]
