Hệ tương đương với:
$\left\{\begin{array}{l}x^3+xy^2-yx^2-y^3=13\\x^3-xy^2+yx^2-y^3=25\end{array}\right.$
$\Leftrightarrow \left\{\begin{array}{l}x^3-y^3=19\\xy(x-y)=6\end{array}\right.$
$\Leftrightarrow \left\{\begin{array}{l}(x-y)[(x-y)^2+3xy]=19\\xy(x-y)=6\end{array}\right.$
$\Leftrightarrow \left\{\begin{array}{l}(x-y)^3=1\\xy(x-y)=6\end{array}\right.$
$\Leftrightarrow \left\{\begin{array}{l}x-y=1\\xy=6\end{array}\right.$
$\Leftrightarrow \left[\begin{array}{l}x=3,y=2\\x=-2,y=-3\end{array}\right.$