$\begin{cases}x-y=10\\\dfrac{-120}{x}+\dfrac{120}{y}=\dfrac{2}{5}\end{cases}\to \begin{cases}x=y+10\\\dfrac{-120}{y+10}+\dfrac{120}{y}=\dfrac{2}{5}\end{cases}\\\to\begin{cases}x=y+10\\-120\times5y+120\times5(y+10)=2y(y+10)\end{cases}\to\begin{cases}x=y+10\\-600y+600y+6000=2y^2+20y\end{cases}\\\to \begin{cases}x=y+10\\y^2+10y-3000=0\end{cases}\to \begin{cases}x=y+10\\\left[\begin{array}{}\hspace{-0,4cm}y=50\\y=-60\end{array}\right.\end{cases}\\\to \left[\begin{array}{}\hspace{-0,5cm}\begin{cases}x=60\\y=50\end{cases}\\\begin{cases}x=-50\\y=-60\end{cases}\end{array}\right.\to(x;y)=(60;\,50);\,(x;y)=(-50;\,-60)$
