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