$1. \begin{cases}(2x+y)^{2}-5(4x^{2}-x^{2})+6(2x-y)^{2}=0 \\ 2x+y+\frac{1}{2x-y}=3 \end{cases}$$2. \begin{cases}y+\frac{3}{2x-y}=2 \\ 5x^{2}+2xy-\frac{1}{(2x+y)^{2}}=2 \end{cases}$$3. \begin{cases}x^{3}+y^{3}-xy^{2}=1 \\ 4x^{4}+y^{4}=4x+y \end{cases}$