Hệ tương đương với:
$\left\{\begin{array}{l}x^3+xy^2-yx^2-y^3=5\\x^3-xy^2+yx^2-y^3=9\end{array}\right.$
$\Leftrightarrow \left\{\begin{array}{l}x^3-y^3=7\\xy(x-y)=2\end{array}\right.$
$\Leftrightarrow \left\{\begin{array}{l}(x-y)[(x-y)^2+3xy]=7\\xy(x-y)=2\end{array}\right.$
$\Leftrightarrow \left\{\begin{array}{l}(x-y)^3=1\\xy(x-y)=2\end{array}\right.$
$\Leftrightarrow \left\{\begin{array}{l}x-y=1\\xy=2\end{array}\right.$
$\Leftrightarrow \left[\begin{array}{l}x=2,y=1\\x=-1,y=-2\end{array}\right.$