coordinate geometry DS problem

In the XY Plane, does the line with equation y = 3x + 2 contain the point (r,s) ?

1. (3r + 2 - s) (4r + 9 - s) = 0
2. (4r - 6 - s) (3r + 2 - s) = 0

Here is my Solution:
This is a yes/no DS problem

For point (r,s) to lie on line with equation y = 3x + 2, it must satisfy this equation i.e., we should be able to get s = 3r + 2

I) (3r + 2 - s) = 0 or (4r + 9 - s) = 0 i.e.,
s = 3r + 2 or ===> Yes
s = 4r + 9 ===> No
Insufficient

II) (4r - 6 - s) = 0 or (3r + 2 - s) = 0
s = 4r - 6 ===> No
s = 3r + 2 ===> Yes
Insufficient


I & II together: This is where i am confused.

If i consider that the common from both statements, then i get answer as C (Both together are sufficient)
In that case what happens to the other two values/equations which are not common in I & II.

I would really appreciate any help to clarify my doubt.

Thanks,
Harmeet.