Thanks for pointing my error - I will re do and post a graphical solution

I do not understand why y=-3 when x=0.
we have the equation 2x+3y<=6, when x=0, y<=3 and when y=0, x<=3. Thus the region R is for all x<3, y<2. The second equation satisfies this condition so i think the answer is B.

Bhattu wrote: So for x=0, y=-2 and x=3, y=0.

thats incorrect. when x=0, y=2.

i strongly feel the answer is B.

The answer is E .

Does anyone have a quick way to getting an answer for this? the suggested solution from the back of the book was very long.

I don know how to draw the graph here.
But by the problem statement, graph wud luk like:-
X axis having 3 as the intercept and Y axis having 2 as intercept and the region covered wud be towards the origin. Lets call this graph1.

By option 1 : X intercept is 2, Y intercept is 3 and the region is towards the origin(say graph2), thus covering both the areas, one inside the graph1 and outside as well. So cannot be determined.

By option 2: Check for point (2.5,1.5) the region is outside graph1, now check for point (0,0) and the region comes out to be inside graph1.
So cannot be determined.

Combining option 1 and 2: Draw X =3 and Y=2, combine with graph2 and still the graph lies both outside and inside graph1.

So answer is E


Doing it graphically took me 2 minutes.