Let (x,y,z) be poitns with integer coordinate satisfying the system of homogeneous equations;
 $\begin{array}{l}3x-y-z=0\\ -3x+z=0\\ -3x+2y+z=0\end{array}$
Then the number of such points for which $x^2+y^2+z^2\le 90$  is

Given ststem of equations  $3x-y-z=0$
                                                   $-3x+z=0$
  And  $-3x+z=0$
Let  $x=p$  where p is an integer, then $y=0$  and  $z=3p$
But  
 
i.e. $p$  can take 7 different values,
$\therefore$  Number of points (x,y,z) are 7