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A system of equations

Source: Vietnam Mathematical Olympiad 2016, Day 1, Problem 1

January 6, 2016
algebra proposedalgebrasystem of equations

Problem Statement

Solve the system of equations {6x−y+z2=3x2−y2−2z=−1emsp;emsp;(x,y,z∈R.)6x2−3y2−y−2z2=0\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}.
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