Durkein

Giải các hệ phương trình sau:

1) $\left\{\begin{matrix} x^{2} + xy + 2y = 2y^{2} + 2x \\ y\sqrt{x-y+1} + x = 2  \end{matrix}\right.$

2) $\left\{\begin{matrix} x^{2} + y^{2} + \frac{2xy}{x+y} = 1 \\ \sqrt{x+y} = x^{2} - y \end{matrix}\right.$

3) $\left\{\begin{matrix} 1 + x^{3}y^{3} = 19x^{3} \\ y + xy^{2} = -6x^{2} \end{matrix}\right.$

4) $\left\{\begin{matrix} \sqrt{3x}(1+\frac{1}{x+y}) = 2 \\ \sqrt{7y}(1-\frac{1}{x+y}) = 4\sqrt{2} \end{matrix}\right.$

5) $\left\{\begin{matrix} x^{2} + y^{2} + xy + 1 = 4y \\ y(x+y)^{2} = 2x^{2} + 7y + 2 \end{matrix}\right.$

6) $\left\{\begin{matrix} y+xy^{2}=6x^{2} \\ 1+x^{2}y^{2}=5x^{2} \end{matrix}\right.$

7) $\left\{\begin{matrix} (x+y)(1+\frac{1}{xy})=5 \\ (x^{2}+y^{2})(1+\frac{1}{x^{2}y^{2}})=49 \end{matrix}\right.$

8) $\left\{\begin{matrix} x^{2}+y+x^{3}y+xy^{2}+xy=-\frac{5}{4} \\ x^{4}+y^{2}+xy(1+2x)=-\frac{5}{4} \end{matrix}\right.$

9) $\left\{\begin{matrix} \sqrt{7x+y} + \sqrt{2x+y} = 5 \\ \sqrt{2x+y}+x-y=2 \end{matrix}\right.$

10) $\left\{\begin{matrix} (4x^{2}+1)x+(y-3)\sqrt{5-2y}=0 \\ 4x^{2}+y^{2}+2\sqrt{3-4x}=7 \end{matrix}\right.$