\(a)xy=1\Rightarrow\orbr{\begin{cases}x=1;y=1\\x=-1;y=-1\end{cases}}\)
\(b)2x+2y-xy=6\)
\(\Rightarrow2x+y\left(2-x\right)=6\)
\(\Rightarrow2x-4+y\left(2-x\right)=6-4\)
\(\Rightarrow-2\left(2-x\right)+y\left(2-x\right)=2\)
\(\Rightarrow\left(2-x\right)\left(y-2\right)=2\)
\(+,\hept{\begin{cases}2-x=1\\y-2=2\end{cases}\Rightarrow\hept{\begin{cases}x=1\\y=4\end{cases}}}\) \(+,\hept{\begin{cases}2-x=-1\\y-2=-2\end{cases}\Rightarrow\hept{\begin{cases}x=3\\y=0\end{cases}}}\)
\(+,\hept{\begin{cases}2-x=2\\y-2=1\end{cases}\Rightarrow\hept{\begin{cases}x=0\\y=3\end{cases}}}\) \(+,\hept{\begin{cases}2-x=-2\\y-2=-1\end{cases}\Rightarrow\hept{\begin{cases}x=4\\y=1\end{cases}}}\)
