In the xy-plane, Region R consists of all the points (x,y) suc that 2x+3y = 6, Is the point (r,s) in the region R?
a) 3r+2s=6
b) r=3 ans s=2.

I beleive that the ans should be B. However it is E.
Can any one explain?

First of all 2x+3y=6 is a straight line, it cannot represent a region. Something is wrong with the question.
2x+3y<6 could represent a region and in that case the answer would be E.

Sorry I meant the answer would be B

yeah, you should check your transcription again.

in fact, statement (2) must be sufficient, regardless of the equation that defines the region. if we are given a definitive set of coordinates - in this case (3, 2) - then that point is either "in" or "out", no matter what region we're considering. therefore, the answer to the question will be either "definitive yes" or "definitive no", so it's sufficient either way.