VMO 2016 Problem 1

Solve the system of equations $\begin{cases}6x-y+z^2=3 x^2-y^2-2z=-1 (x,y,z\in\mathbb{R}.) 6x^2-3y^2-y-2z^2=0\end{cases}$ .

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.