\(2\left(x+y\right)=xy+2\\ \Leftrightarrow2x+2y-xy-2=0\\ \Leftrightarrow x\left(2-y\right)+-2\left(2-y\right)+2=0\\ \Leftrightarrow\left(x-2\right)\left(2-y\right)=-2\\ \Leftrightarrow\left(x-2\right)\left(y-2\right)=2\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-2=1\\y-2=2\end{matrix}\right.\\\left\{{}\begin{matrix}x-2=-1\\y-2=-2\end{matrix}\right.\\\left\{{}\begin{matrix}x-2=2\\y-2=1\end{matrix}\right.\\\left\{{}\begin{matrix}x-2=-2\\y-2=-1\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=3\\y=4\end{matrix}\right.\\\left\{{}\begin{matrix}x=1\\y=0\end{matrix}\right.\\\left\{{}\begin{matrix}x=4\\y=3\end{matrix}\right.\\\left\{{}\begin{matrix}x=0\\y=1\end{matrix}\right.\end{matrix}\right.\)
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