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I assumed that there was a mistake in statement 1, it should be
(1) 3r + 2s = 6
if not it doesn't seem correct, r is an abscyss and x too

I would choose B because statement 1 just tell us the equation of one line and not where is the point (r,s).

With statement1, we can see that the line with equation 3r + 2s = 6 is crossing the line with equation 2x + 3y = 6 so there is one common point that can satisfy both equation but we don't know if (r,s) is this point or any other.

statement 2 let us know where is the point and it's clearly not in the line with equation 2x + 3y = 6 so we can answer NO

However, I am confused, I am not sure one single line can be considered as a region, I thought a region would have been defined more like 2x + 3y > 6 or 2x + 3y < 6

I assumed that there was a mistake in statement 1, it should be (1) 3r + 2s = 6 if not it doesn't seem correct, r is an abscyss and x too

I would choose B because statement 1 just tell us the equation of one line and not where is the point (r,s).

With statement1, we can see that the line with equation 3r + 2s = 6 is crossing the line with equation 2x + 3y = 6 so there is one common point that can satisfy both equation but we don't know if (r,s) is this point or any other.

statement 2 let us know where is the point and it's clearly not in the line with equation 2x + 3y = 6 so we can answer NO

However, I am confused, I am not sure one single line can be considered as a region, I thought a region would have been defined more like 2x + 3y > 6 or 2x + 3y < 6

I think the reason the answer is E because nowhere in the qtn(I am assuming that is the full text of the qtn) have they defined Region R. By assuming that R is the region formed by the X axis, y axis and this third line we have all erred.

I think the reason the answer is E because nowhere in the qtn(I am assuming that is the full text of the qtn) have they defined Region R. By assuming that R is the region formed by the X axis, y axis and this third line we have all erred.

I guess So!!!!!

I believe OA is wrong, ques says that the straight line in XY plane creates a region, a region doesn't neccessarily have to have 2 lines, curve etc. A straight line is a region as well, however infinitely small it may be.

Just a question but can you define a plan by an equation for a line? If you plot the equation 2x+3y = 6 you get a line through which can draw an infinite number of planes right? SO unless (r,s) is on the line itself you really cannot know if it is on the plane right? Could that be why the answer is E?
_________________

I go with B, since the region R is defined by a straight line, and r,s is on this line.

statement 1 is not enough to say that (r,s) is on the same line as (x,y) since it defines a different line. It may intersect with R but it's not certain with just statement 1. Statement 2 gives a set of values for r,s so we know for sure it's on R.
_________________

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

(1) 3r + 2s = 6

(2) r=3 and s=2

I also came out with b
1. point (r, s) may or may not be in region R, as these two lines do in fact intersect -- insufficient
2. point's exact coordinates are revealed, so this is sufficient

I think it's important that we get to the bottom of this question

I go with B, since the region R is defined by a straight line, and r,s is on this line.

statement 1 is not enough to say that (r,s) is on the same line as (x,y) since it defines a different line. It may intersect with R but it's not certain with just statement 1. Statement 2 gives a set of values for r,s so we know for sure it's on R.

That's what I thought too. Doesn't the 1st statement just give another line and not any information about what points r and s are?