\(\left(x-7\right).\left(xy+1\right)=9\)
\(\Rightarrow\left(x-7\right).\left(xy+1\right)=1.9=9.1=\left(-1\right).\left(-9\right)=\left(-9\right).\left(-1\right)=3.3=\left(-3\right).\left(-3\right)\)
\(TH1:\hept{\begin{cases}x-7=1\\xy+1=9\end{cases}\Rightarrow\hept{\begin{cases}x=8\\y=1\end{cases}}}\)
\(TH2:\hept{\begin{cases}x-7=9\\xy+1=1\end{cases}}\Rightarrow\hept{\begin{cases}x=16\\y=0\end{cases}}\)
\(TH3:\hept{\begin{cases}x-7=-1\\xy+1=-9\end{cases}}\Rightarrow\hept{\begin{cases}x=6\\y=\frac{-10}{6}\left(\text{loại}\right)\end{cases}}\)
\(TH4:\hept{\begin{cases}x-7=-9\\xy+1=-1\end{cases}}\Rightarrow\hept{\begin{cases}x=-2\\y=1\end{cases}}\)
\(TH4:\hept{\begin{cases}x-7=3\\xy+1=3\end{cases}}\Rightarrow\hept{\begin{cases}x=10\\y=\frac{2}{10}\left(\text{loại}\right)\end{cases}}\)
\(TH5:\hept{\begin{cases}x-7=-3\\xy+1=-3\end{cases}}\Rightarrow\hept{\begin{cases}x=4\\y=-1\end{cases}}\)
\(\text{Vậy :}\left(x;y\right)\in\left\{\left(8;1\right);\left(16;0\right);\left(-2;1\right);\left(4;-1\right)\right\}\)
