Given the system of equations:
[tex]\begin{cases}-2x-y=12 \\ y=-26-9x\end{cases}[/tex]We can rewrite the second equation:
[tex]\begin{cases}-2x-y=12 \\ 9x+y=-26\end{cases}[/tex]Now, we can add these two equations, canceling the variable y:
[tex]\begin{gathered} -2x-y+9x+y=12-26 \\ 7x=-14 \\ \Rightarrow x=-2 \end{gathered}[/tex]Now, we can use this result to find the value of y. Using the second equation:
[tex]\begin{gathered} 9\cdot(-2)+y=-26 \\ -18+y=-26 \\ y=-26+18 \\ \Rightarrow y=-8 \end{gathered}[/tex]The solution is:
[tex]\begin{gathered} x=-2 \\ y=-8 \end{gathered}[/tex]