Ta có :
\(xy+3x-2y-6=5\)
\(\Leftrightarrow x\left(y+3\right)-2\left(y+3\right)=5\)
\(\Leftrightarrow\left(x-2\right)\left(y-3\right)=5\)
Vì \(x,y\in Z\Leftrightarrow x-2,y+3\in Z\)
\(\Leftrightarrow x-2,y+3\inƯ\left(5\right)\)
Ta có các trường hợp :
+) \(\left\{{}\begin{matrix}x-2=1\\y+3=5\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=2\end{matrix}\right.\)
+) \(\left\{{}\begin{matrix}x-2=5\\y+3=1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=7\\y=-2\end{matrix}\right.\)
+) \(\left\{{}\begin{matrix}x-2=-1\\y+3=-5\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=-8\end{matrix}\right.\)
+) \(\left\{{}\begin{matrix}x-2=-5\\y+3=-1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=-3\\y=-4\end{matrix}\right.\)
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