1.\begin{cases}x^4-y^4=\frac{3}{4y}-\frac{1}{2x} \\ (x^2-y^2)^5+5=0 \end{cases}
2.\begin{cases}x^3+3x^2+4x+2=y+\sqrt[3]{y} \\ x^3-\sqrt{3}.x^2+3\sqrt[3]{y}=3+\sqrt{3} \end{cases}
3.\begin{cases}3x^6+7x^4.y^2-7x^2.y^4-3y^6=\frac{2}{y} -\frac{3}{2x}\\ (x^2-y^2)^7+7=0 \end{cases}
4.\begin{cases}2x^2-\frac{2}{y^2}-(\sqrt{2}+1)(x\sqrt{2}-1)-\frac{xy^2}{x^2y^2+1}=0 \\ 4x+\frac{y^2}{x^2y^2+1}= 2+\sqrt{2}\end{cases}
5.\begin{cases}x+\frac{x^3}{x+1}=(y+2)\sqrt{(1+x)(1+y)} \\ 4x\sqrt{y+1}+8x= (4x^2-4x-3)\sqrt{x+1}\end{cases}