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

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

In case 1, one of 2 brackets can be 0. If 3r+2-s = 0 then yes, line contains the point. Is 2nd bracket value is 0 , there is one valuse of r and s on which it does, but not for each value of r and s.

Same for case 2.

Coombined together, if both are true, 4r+9-s and 4r-6-S, can not both be 0 at the same time. So 3r+2-S = 0. This is same as y=3x+2. So if 3r+2-s = 0, this line will contain every (R,S) satisfying this equation.

So C is the answer. What is OA?

(C) is the right answer. Great explanation!

Could you please elaborate or clarify by what you mean when you say, "Combined together, if both are true, 4r+9-s and 4r-6-S, cannot both be 0 at the same time." Why is this so?

Thanks

yes, can you please further explain the steps? for example, why are there only unique values for one of the brackets but not both for statements 1 & 2? also, isn't 3r+2-s a reiteration of the equation y=3x+2? but not sure how that answers the question and concludes that the line contains the coordinates (r,s). in sum, if you can just explain this a little more thoroughly it would be greatly appreciated! thanks.

("4r-s"+9) and ("4r-s"-6) can not both be Zero...

Great solution, anadi. I'll give it a go, too.



Question: Does s = 3r + 2? Or, put another way, does 3r +2 - s = 0?

(1) Each of these factors may equal zero, so we know that either 3r + 2 - s = 0 OR that 4r + 9 - s = 0. Insufficient.
(2) Similarly, we know that either 4r - 6 - s = 0 OR that 3r + 2 - s = 0. Insufficient.
(1&2) The only possibility that would satisfy both statements is that 3r + 2 - s = 0. Sufficient.