1.$\left\{\begin{matrix} 2x+4y+\frac{x}{y}+\frac{y}{x}=8 & & \\4x+\frac{1}{x}+\frac{1}{y}=6 & & \end{matrix}\right.$
2.$\left\{\begin{matrix} 1+x+xy=5y & & \\1+x^{2}+y^{2}=5y^{2} & & \end{matrix}\right.$
3.$\left\{\begin{matrix} -2x^{2}+xy(1-x)+2(x-y)-4=0 & & \\ 2x^{4}-2x^{3}-5(x+y)^{2}-21(x+y)=16 & & \end{matrix}\right.$
4.$\left\{\begin{matrix} 8y^{2}+4xy+2x+1=0 & & \\ (x+y)^{2}-y-3x=1 & & \end{matrix}\right.$
5.$\left\{\begin{matrix} \sqrt[3]{2x-y}+\sqrt{x-2y}=6 & & \\5(x^{2}-xy+y^{2})=3(xy-81) & & \end{matrix}\right.$
6.$\left\{\begin{matrix} x^{4}+2x^{3}+2x^{2}+2x+1=x^{2}y & & \\y^{2}x+2xy=1+x^{2} & & \end{matrix}\right.$
7.$\left\{\begin{matrix} (9x^{2}+2)x+(y-2)\sqrt{4-3y}=0 & & \\9x^{2}+y^{2}+\frac{4}{3}\sqrt{2-3x}=\frac{10}{3} & & \end{matrix}\right.$
8.$\left\{\begin{matrix} x^{4}+4x^{2}y=6y^{3}+y^{2}+2 & & \\ 3(x^{2}+2y)^{2}+3y^{3}=y^{2}-1 & & \end{matrix}\right.$
9.$\left\{\begin{matrix} (x-y)(y^{2}+y+1-x)=y^{2} & & \\(x-y)^{2}(y^{4}+1)=2y^{4} & & \end{matrix}\right.$
10.$\left\{\begin{matrix} 2(2-x^{2})+9x^{2}y^{2}=0 & & \\ 4(\frac{1}{x}-3y)+9xy^{2}=0 & & \end{matrix}\right.$