Let (x,y,z) be points with integer coordinates satisfying the system of homogeneous equations : 3x−y−z=0...(i) −3x+z=0...(ii) −3x+2y+z=0...(iii) Then, the number of such points for which x2+y2+z2≤100, is
A
6
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B
7
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C
49
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D
none of these
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Solution
The correct option is B7 3x−y−z=0...(1) −3x+z=0...(2) −3x+2y+z=0...(3) adding (1) and (2) gives y=0 but from (2) ⇒3x=z ∴ solution for the given set of equations is (x,y,z)=(t,0,3t) where t is an integer. For, x2+y2+z2≤100 ⇒10t2≤100 ⇒t2≤10 ∴ possible values of t are −3,−2,−1,0,1,2,3 i.e 7 possible solutions. Hence, option B.