Giải các hệ phương trình:

$$\begin{gathered} a)\left\{\begin{array}{l}2x+3\left|y\right|=13\\ 3x-y=3\end{array}\right.; \\ b) \left\{\begin{array}{l}3\sqrt{x}-2\sqrt{y}=-2\\ 2\sqrt{x}+\sqrt{y}=1\end{array}\right. \end{gathered}$$

Giải: 

a) Trường hợp $y\ge 0$ hệ đã cho trở thành

$$\begin{gathered} \left\{\begin{array}{l}2x+3y=13\\ 3x-y=3\end{array}\right.\iff \left\{\begin{array}{l}2x+3y=13\\ 9x-3y=9\end{array}\right.\iff \left\{\begin{array}{l}11x=22\\ 2x+3y=13\end{array}\right. \\ \iff \left\{\begin{array}{l}x=2\\ 3y=13-2.2\end{array}\right.\iff \left\{\begin{array}{l}x=2\\ y=3\end{array}\right. \end{gathered}$$

Trường hợp $y<0$ hệ đã cho trở thành

$$\begin{gathered} \left\{\begin{array}{l}2x-3y=13\\ 3x-y=3\end{array}\right.\iff \left\{\begin{array}{l}2x-3y=13\\ 9x-3y=9\end{array}\right.\iff \left\{\begin{array}{l}7x=-4\\ 9x-3y=9\end{array}\right. \\ \iff \left\{\begin{array}{l}x=-\frac{4}{7}\\ -3y=9-9\left(-\frac{4}{7}\right)\end{array}\right.\iff \left\{\begin{array}{l}x=-\frac{4}{7}\\ -3y=\frac{99}{7}\end{array}\right.\iff \left\{\begin{array}{l}x=-\frac{4}{7}\\ y=-\frac{33}{7}\end{array}\right. \end{gathered}$$

Vậy: Trường hợp $y\ge 0$, hệ có nghiệm $x=2, y=3$.

Trường hợp $y<0$, hệ có nghiệm $x=-\frac{4}{7}, y=-\frac{33}{7}$

b) Đặt $\sqrt{x}=X\ge 0, \sqrt{y}=Y\ge 0$ ta được hệ:

$$\begin{gathered} \left\{\begin{array}{l}3X-2Y=-2\\ 2X+Y=1\end{array}\right.\iff \left\{\begin{array}{l}3X-2Y=-2\\ 4X+2Y=2\end{array}\right.\iff \left\{\begin{array}{l}7X=0\\ 2Y=2\end{array}\right.\iff \left\{\begin{array}{l}X=0\\ Y=1\end{array}\right. \\ \iff \left\{\begin{array}{l}\sqrt{x}=0\\ \sqrt{y}=1\end{array}\iff \left\{\begin{array}{l}x=0\\ y=1\end{array}\right.\right. \end{gathered}$$