`xy-x-y=0`
`<=>xy-x-y+1=1`
`<=> x(y-1)-(y-1)=1`
`<=> (y-1)(x-1)=1`
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}y-1=1\\x-1=1\end{matrix}\right.\\\left\{{}\begin{matrix}y-1=-1\\x-1=-1\end{matrix}\right.\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}y=2\\x=2\end{matrix}\right.\\\left\{{}\begin{matrix}y=0\\x=0\end{matrix}\right.\end{matrix}\right.\)