Given the system of equations :
[tex]\begin{gathered} 8x+6y=-36 \\ 9y=-8x-66 \end{gathered}[/tex]arranging like terms
so,
[tex]\begin{gathered} 8x+6y=-36 \\ 8x+9y=-66 \end{gathered}[/tex]Subtract the first equation from the second equation :
[tex]\begin{gathered} (8x+9y)-(8x+6y)=-66-(-36) \\ 8x+9y-8x-6y=-66+36 \\ (8x-8x)+(9y-6y)=-30 \\ 3y=-30 \\ \\ y=-\frac{30}{3}=-10 \end{gathered}[/tex]Substitute with y at the first equation to find x
[tex]\begin{gathered} 8x+6\cdot-10=-36 \\ 8x-60=-36 \\ 8x=60-36 \\ 8x=24 \\ \\ x=\frac{24}{8}=3 \end{gathered}[/tex]So, the solution of the system is:
[tex]\begin{gathered} x=3 \\ y=-10 \end{gathered}[/tex]