DK-GEORGMOHR 2009 Problem 2

Solve the system of equations $\begin{cases} \dfrac{1}{x+y}+ x = 3 \dfrac{x}{x+y}=2 \end{cases}$

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.