1.$\left\{\begin{matrix} 2y=x^3+1 & \\ 3y-\frac{1}{y}=x^3+x-\frac{1}{x} & \end{matrix}\right.$
2.$\left\{\begin{matrix} xy-3x-2y+6=0& \\ x^2+y^2-2x-4y+3=0 & \end{matrix}\right.$
3.$\left\{\begin{matrix} \sqrt{2x+y+5}-\sqrt{3-x-y}=x^3-3x-10y+6 & \\ x^3-6x^2+13x=y^3+y+10& \end{matrix}\right.$
4.$\left\{\begin{matrix} x^3-x^2y=x^2-x+y+1 & \\ x^3-9y^2+6(x-3y)-15=3\sqrt[3]{6x^2+2} & \end{matrix}\right.$