$\left\{\begin{matrix}
& x^2+y^2+x^2y^2=1+2xy & \\
& (x-y)(1+xy)=1-xy &
\end{matrix}\right.$
$\left\{\begin{matrix}
& \sqrt{x+1}+\sqrt{y-1}=4 & \\
& \sqrt{x+6}+\sqrt{y+4}=6 &
\end{matrix}\right.$
$\left\{\begin{matrix}
& \sqrt{x^2+y^2}+\sqrt{2xy}=8.\sqrt{2} & \\
& \sqrt{x}+\sqrt{y}=4 &
\end{matrix}\right.$