\(x-y+2xy=7\)
\(\Leftrightarrow2x-2y+4xy=7.2\)
\(\Leftrightarrow2x-2y+4xy=14\)
\(\Leftrightarrow2x-1+2xy-2y=14-1\)
\(\Leftrightarrow\left(2x-1\right)+2y\left(2x-1\right)=13\)
\(\Leftrightarrow\left(2x-1\right)\left(2y+1\right)=13\)
\(\Leftrightarrow2x-1;2y+1\inƯ\left(13\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}2x-1=13\\2y+1=1\end{matrix}\right.\\\left\{{}\begin{matrix}2x-1=1\\2y+1=13\end{matrix}\right.\\\left\{{}\begin{matrix}2x-1=-13\\2y+1=-1\end{matrix}\right.\\\left\{{}\begin{matrix}2x-1=-1\\2y+1=-13\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=7\\y=0\end{matrix}\right.\\\left\{{}\begin{matrix}x=1\\y=6\end{matrix}\right.\\\left\{{}\begin{matrix}x=-6\\y=-1\end{matrix}\right.\\\left\{{}\begin{matrix}x=0\\y=-7\end{matrix}\right.\end{matrix}\right.\)
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