\(\Leftrightarrow xy-x-y+1=-11\)
\(\Leftrightarrow x\left(y-1\right)-\left(y-1\right)=-11\)
\(\Leftrightarrow\left(x-1\right)\left(y-1\right)=-11\)
TH1: \(\left\{{}\begin{matrix}x-1=11\\y-1=-1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=12\\y=0\end{matrix}\right.\)
TH2 \(\left\{{}\begin{matrix}x-1=-1\\y-1=11\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=0\\y=12\end{matrix}\right.\)