Count all the points

Algebra Level 3

Let \((x,y,z)\) be points with integer co-ordinates satisfying the system of homogeneous equations \[\begin{cases} 3x-y-z=0 \\ -3x+z=0 \\ -3x+2y+z=0 \end{cases}\] Find the number of such points for which \(x^2+y^2+z^2 \leq 100\)

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