Hi,

For the point (r,s) to belong to the line: y = 3x+2 then

s = 3r + 2, or

3r + 2 - s = 0


1. As (3r + 2 - s )( 4r + 9 - s) = 0, then

either (3r + 2 - s) or (4r + 9 - s) can be equal to Zero. So we cannot define whether (3r + 2 - s) is equal to Zero.

Hence, 1 is insuff.


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

The same as 1, either (3r + 2 - s) or (4r - 6 - s) can be equal to Zero

Hence, 2 is insuff.

1&2
either (3r + 2 - s) or (4r + 9 - s) can be equal to Zero
AND
either (3r + 2 - s) or (4r - 6 - s) can be equal to Zero

Then 3r + 2 - s must be equal to Zero. Why?

As both (4r + 9 - s) and (4r - 6 - s) cannot be equal to Zero, or - say in another way:
4r - s cannot be both -9 and 6.

Then point (r,s) belong to the above line. Thus 1&2 is suff.

Pick C