\(x+y=xy+1\)
\(\Rightarrow x+y-xy-1=0\)
\(\Rightarrow\left(x-xy\right)+\left(y-1\right)=0\)
\(\Rightarrow x\left(1-y\right)+\left(y-1\right)=0\)
\(\Rightarrow x\left(1-y\right)-\left(1-y\right)=0\)
\(\Rightarrow\left(1-y\right)\left(x-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}1-y=0\\x-1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}y=1\\x=1\end{matrix}\right.\)
