$\left\{\begin{matrix}\sqrt{2xy-3}\bigg(1-\dfrac{3}{2xy-3}\bigg)=2\ (1)\\y(x-y)=-3\ (2)\end{matrix}\right.$
Đặt $a=\sqrt{2xy-3}\ (a>0)$
$(1)\Leftrightarrow a\bigg(1-\dfrac{3}{a^2}\bigg)=2\\\Leftrightarrow a-\dfrac{3}{a}=2\\\Leftrightarrow a^2-2a-3=0\\\Leftrightarrow \left[\begin{matrix}a=-1\ (l)\\a=3\ (t/m)\end{matrix}\right.$
$a=3\Rightarrow \sqrt{2xy-3}=3\\\Leftrightarrow 2xy-3=9\\\Leftrightarrow xy=6$
$(2)\Leftrightarrow xy-y^2=-3\\\Leftrightarrow y^2=xy+3=9\Rightarrow y=\pm3$
$y=-3\Rightarrow x=-2$
$y=3\Rightarrow x=2$
Vậy hpt có 2 nghiệm $(-2;-3)\ và\ (2;3)$
