\(xy-3x-y=0\)
\(\Rightarrow xy-3x-y+3=3\)
\(\Rightarrow x\left(y-3\right)-1\left(y-3\right)=3\)
\(\Rightarrow\left(x-1\right)\left(y-3\right)=3\)
\(\Rightarrow x-1;y-3\in U\left(3\right)\)
\(U\left(3\right)=\left\{\pm1;\pm3\right\}\)
\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-1=1\Rightarrow x=2\\y-3=3\Rightarrow y=6\end{matrix}\right.\\\left\{{}\begin{matrix}x-1=-1\Rightarrow x=0\\y-3=-3\Rightarrow y=0\end{matrix}\right.\\\left\{{}\begin{matrix}x-1=3\Rightarrow x=4\\y-3=1\Rightarrow y=4\end{matrix}\right.\\\left\{{}\begin{matrix}x-1=-3\Rightarrow x=-2\\y-3=-1\Rightarrow y=2\end{matrix}\right.\end{matrix}\right.\)
