Adding first two equations, we get y=0
and substituting y=0 in third equation, we get, z=3x
So any point which satisfies given system can be taken as, (a,0,3a)
Now for this point to lie inside inside a sphere of radius 10 centered at origin.
So, possible integral values of a are −3,−2,−1,0,1,2,3
Hence, number of such points is 7.