`<=> x(y+1) + y + 1 = 0`
`<=> (x+1)(y+1)=0`
`<=>` \(\left[{}\begin{matrix}x+1=0\\y+1=0\end{matrix}\right.\)
`<=>` \(\left[{}\begin{matrix}x=-1\\y=-1\end{matrix}\right.\)
\(...\Leftrightarrow x\left(y+1\right)+y+1=0\Leftrightarrow\left(x+1\right)\left(y+1\right)=0\) \(\Leftrightarrow\left[{}\begin{matrix}x=-1\\y=-1\end{matrix}\right.\)
x.y+x+y+1=0x.y+x+y+1=0
(x+1).y+x+1=0(x+1).y+x+1=0
(x+1).y+x-0+1=0(x+1).y+x-0+1=0
(x+1).(y+1)=0(x+1).(y+1)=0
x+1=0x+1=0
x=-1x=-1
y+1=0y+1=0
y=-1