1. $\left\{ \begin{array}{l} x^{4}-2x^{2}y+2y^{2}-1=0\\ x^{2} y^{2}-y^{3}+x^{2}-y^{2}-y+1 = 0\end{array} \right.$
2. $\left\{ \begin{array}{l} x-2y-\sqrt{xy}=0\\ \sqrt{x-1}+\sqrt{4y-1}=2 \end{array} \right.$
3. $\left\{ \begin{array}{l} x+y+\sqrt{x^{2}-y^{2}}=12\\ y\sqrt{x^{2}-y^{2}}=12 \end{array} \right.$