4. Solve the system of equations: $\left\{\begin{array}{l}x^{2}-y=z^{2}, \\ y^{2}-z=x^{2}, \\ z^{2}-x=y^{2} .\end{array}\right.$
(2013, Croatian Mathematical Competition)
提示 三个方程相加得 $x+y+z=0$.
代人消元得
$$
\begin{aligned}
(x, y, z)= & (1,0,-1),(0,0,0), \\
& (0,-1,1),(-1,1,0) .
\end{aligned}
$$

Translation:
Adding the three equations yields $x+y+z=0$.
Substituting and eliminating variables, we get
$$
\begin{aligned}
(x, y, z)= & (1,0,-1),(0,0,0), \\
& (0,-1,1),(-1,1,0) .
\end{aligned}
$$