JEE Advanced 2009 Mathematics question

Let (x, y, z) be points with integer coordinates satisfying the system of homogeneous equations:

3x - y - z = 0

-3x + z = 0

-3x + 2y + z = 0.

Then the number of such points for which is

Answer: 7

Solution

From the second equation z = 3x; the first then gives y = 3x − z = 0, and the third is satisfied: −3x + 0 + 3x = 0. The

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Question ID VK-037762