\(\left\{{}\begin{matrix}x^2y+y^3=x^4+x^6\\\left(x+2\right)\sqrt{y+1}=\left(x+1\right)^2\end{matrix}\right.\)

\(\left\{{}\begin{matrix}x+\sqrt{x^2-2x+2}=3^{y-1}+1\\y+\sqrt{y^2-2y+2}=3^{x-1}+1\end{matrix}\right.\)

\(\left\{{}\begin{matrix}4xy+4\left(x^2+y^2\right)+\frac{3}{\left(x+y\right)^2}=7\\2x+\frac{1}{x+y}=3\end{matrix}\right.\)

\(\left\{{}\begin{matrix}\sqrt{x+y}+\sqrt{x-y}=1+\sqrt{x^2-y^2}\\\sqrt{x}+\sqrt{y}=1\end{matrix}\right.\)

\(\left\{{}\begin{matrix}\sqrt{x+y}+\sqrt{x+3}=\frac{y-3}{x}\\\sqrt{x+y}+\sqrt{x}=x+3\end{matrix}\right.\)

\(\left\{{}\begin{matrix}2x^2+2y^2=1+2x+y\\2y^2+2x+y+1=6xy\end{matrix}\right.\)