Problem

Source: 2024 Israel National Olympiad (Gillis) P1

Tags: algebra, system of equations, national olympiad



Solve the following system (over the real numbers): \[\begin{cases}5x+5y+5xy-2xy^2-2x^2y=20 &\\ 3x+3y+3xy+xy^2+x^2y=23&\end{cases}\]