y=3x+2 containing the point (r,s) means that s = 3r + 2.
(1) Tells us that 3r + 2 - s = 0 OR 4r + 9 - s = 0.
3r + 2 - s = 0 gives us s = 3r + 2. But this can also be satisfied from s = 4r + 9 (from 4r + 9 - s = 0)
So this is not sufficient.
(2) Similarly, we get 4r - 6 - s = 0 OR 3r + 2 - s = 0. Solving for s we get s = 4r - 6 OR s = 3r + 2
So this is not sufficient.
(1)+(2) s = 3r + 2 is the only factor that satisfies BOTH 1 and 2 so s = 3r + 2.
So the answer is C.
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