1. \begin{cases}(2x^{2}-3x+4)(2y^{2}-3y+4)=18 \\ x^{2}+y^{2}+xy+-7x-6y+14=0 \end{cases}
2. \begin{cases}(x-2010)(2011+2012\sqrt[3]{y-2013}=1 \\ (y-4024)\sqrt[3]{x-2010}=201 2 \end{cases}
3. \begin{cases}2x^{2}y+3xy=4x^{2}+9y \\ 7y+6=2x^{2}+9x \end{cases}
4.\begin{cases}2-\sqrt{x^{2}y^{4}+2xy^{2}-y^{4}+1}=2y^{2}(3-x-\sqrt{2}) \\ x(y^{3}-x^{3})=7 \end{cases}
5. \begin{cases}(x^{2}+y^{2}-7)(x+y)^{2}+2=0 \\ (x-3)(x+y)+1=0 \end{cases}