DE-MO 2015 Problem 1

Determine all pairs of real numbers $(x,y)$ satisfying \begin{align*} x^3+9x^2y&=10, y^3+xy^2 &=2. \end{align*}

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.