1. $\begin{cases}x^{3}+2y^{2}=x^{2}y+2xy \\ 2\sqrt{x^{2}-2y-1}+\sqrt[3]{y^{3}-14}=x-2 \end{cases}$
2. $\begin{cases}16x^{2}+4xy+y^2=12 \\ 8x^2+4xy-28x-5y=-18 \end{cases}$
3. $\begin{cases}\frac{x^{2}+y^{2}}{xy}+\frac{2}{x+y}=\frac{1}{xy} \\ x^{2}+y^{2}-\frac{1}{x+y}=-x^{2}+2x+1 \end{cases}$