\(xy+5x-3y-13=0\)
\(\Leftrightarrow xy+5x-3y-15=-2\)
\(\Leftrightarrow x\left(y+5\right)-3\left(y-5\right)=-2\)
\(\Leftrightarrow\left(y+5\right)\left(x-3\right)=-2\)
Vì \(x,y\in Z\Rightarrow\left(y+5\right);\left(x-3\right)\inƯ\left(-2\right)\)
\(TH1:\left\{{}\begin{matrix}y+5=-1\\x-3=2\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{7}{8}\\y=-\dfrac{3}{8}\end{matrix}\right.\)(loại)
\(TH2:\left\{{}\begin{matrix}y+5=1\\x-3=-2\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{7}{8}\\y=\dfrac{3}{8}\end{matrix}\right.\)(loại)
Vậy phương trình đã cho vô nghiệm.
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