Let \( (x, y, z) \) be points with integer coordinates satisfying the system of homogeneous equa...

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Let \( (x, y, z) \) be points with integer coordinates satisfying the system of homogeneous equations:
\[
\begin{array}{l}
3 x-y-z=0 \\
-3 x+z=0 \\
-3 x+2 y+z=0
\end{array}
\]
Then the number of such points for which \( x^{2}+y^{2}+z^{2} \leq 100 \) is
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