The given system is
[tex]\begin{cases}x-9y=20 \\ -8x+18y=2\end{cases}[/tex]First, we multiply the first equation by 8
[tex]\begin{cases}8x-72y=160 \\ -8x+18y=2\end{cases}[/tex]Then, we combine the equations
[tex]\begin{gathered} 8x-8x-72y+18y=160+2 \\ -54y=162 \\ y=\frac{162}{-54} \\ y=-3 \end{gathered}[/tex]Now, we find x
[tex]\begin{gathered} x-9y=20 \\ x-9(-3)=20 \\ x+27=20 \\ x=20-27 \\ x=-7 \end{gathered}[/tex]