Hệ phương trình tương đương với:
$\left\{\begin{array}{l}x^2+xy=3\\y^3+xy^2+3(x-2y)=0\end{array}\right.$
$\Leftrightarrow \left\{\begin{array}{l}x^2+xy=3\\y^3+xy^2+(x^2+xy)(x-2y)=0\end{array}\right.$
$\Leftrightarrow \left\{\begin{array}{l}x^2+xy=3\\x^3-x^2y-xy^2+y^3=0\end{array}\right.$
$\Leftrightarrow \left\{\begin{array}{l}x^2+xy=3\\(x-y)^2(x+y)=0\end{array}\right.$
$\Leftrightarrow \left\{\begin{array}{l}x=y\\x^2+xy=3\end{array}\right.$
$\Leftrightarrow \left[\begin{array}{l}x=y=\sqrt{\dfrac{3}{2}}\\x=y=-\sqrt{\dfrac{3}{2}}\end{array}\right.$