\(\begin{cases}\dfrac{1}{2}(x+2)(y+3)-\dfrac{1}{2}xy=50\\\dfrac{1}{2}xy-\dfrac{1}{2}(x-2)(y-2)=32\end{cases}\to\begin{cases}\dfrac{1}{2}(xy+3x+2y+6)-\dfrac{1}{2}xy=50\\\dfrac{1}{2}xy-\dfrac{1}{2}(xy-2x-2y+4)=32\end{cases}\\\to \begin{cases}\dfrac{3}{2}x+y+3=50\\x+y-2=32\end{cases}\to \begin{cases}3x+2y=94\\x+y=34\end{cases}\\\to \begin{cases}3x+2y=94\\2x+2y=68\end{cases}\to \begin{cases}x=26\\26+y=34\end{cases}\\\to \begin{cases}x=26\\y=8\end{cases}\to(x;\,y)=(26;\,8)\)
