1)$\left\{\begin{matrix} xy+x+y=x^{2}-2y^{2} & & \\ x\sqrt{2y}-y\sqrt{x-1}=2x-2y & & \end{matrix}\right.$
2)$\left\{\begin{matrix} x^{4}+2x^{3}y+2x^{2}y^{2}=2x+9 & & \\ x^{2}+2xy=6x+6 & & \end{matrix}\right.$
3)$\left\{\begin{matrix} x^{2}+y^{2}+xy+1=4y & & \\ (x^{2}+1)(x+y-2)=y & & \end{matrix}\right.$
4)$\left\{\begin{matrix} xy+2=3x^{3} & & \\2xy^{3}-3x=-y^{2} & & \end{matrix}\right.$
5)$\left\{\begin{matrix} 1+xy+\sqrt{xy}=x & & \\ \frac{1}{x\sqrt{x}}+y\sqrt{y}=\frac{1}{\sqrt{x}}+3\sqrt{y} & & \end{matrix}\right.$
6)$\left\{\begin{matrix} x^{4}+y^{4}=x^{3}y+xy^{3}& & \\ \sqrt{4-x}+\sqrt{y+1}-\sqrt{3x-x^{2}+4}=1 & & \end{matrix}\right.$
7)$\left\{\begin{matrix} x^{2}+2x+y^{2}+y=3-xy & & \\ xy+x+2y=1 & & \end{matrix}\right.$
8)$\left\{\begin{matrix} x^{3}-6x^{2}y+9xy^{2}-4y^{3}=0 & & \\ \sqrt{x-y}+\sqrt{x+y}=2 & & \end{matrix}\right.$
9)$\left\{\begin{matrix} x+3y+3\sqrt{xy+y^{2}}=xy+y^{2}+y\sqrt{x+y} & & \\x+y=xy+x^{2} & & \end{matrix}\right.$
10)$\left\{\begin{matrix} x(x+1)+\frac{1+y}{y^{2}}=4 & & \\ (xy+1) (x^{2}y^{2}+1)-4y^{3}=0 & & \end{matrix}\right.$
11)$\left\{\begin{matrix} x^{4}+x^{2}y^{2}-y^{2}=y^{3}+x^{2}y+x^{2} & & \\2y^{3}-\sqrt{5-2x^{2}}-1=0 & & \end{matrix}\right.$