In the xy-plane, region R consists of all the points (x, y) : DS Archive
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# In the xy-plane, region R consists of all the points (x, y)

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23 Sep 2007, 07:48
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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
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23 Sep 2007, 09:04
its E..

we dont know if the region is below the line or above the line...

what is the region???
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23 Sep 2007, 09:56
Since the second statement is sufficient to conclude. Statement 1 is inconclusive
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23 Sep 2007, 10:01
gmatter2008 wrote:
Since the second statement is sufficient to conclude. Statement 1 is inconclusive

How is the second statement sufficient? Is (r,s) on the line 2x + 3y = 6 or not?

Why is statement 1 inconclusive?
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24 Sep 2007, 10:06
gluon wrote:
gmatter2008 wrote:
Since the second statement is sufficient to conclude. Statement 1 is inconclusive

How is the second statement sufficient? Is (r,s) on the line 2x + 3y = 6 or not?

Why is statement 1 inconclusive?

go for B,

1st- insuff. Could be YES/NO
Do not get confused over (r,s) it is the same as (x,y) but in diff. equation.

i think the best ways to solve for the fisrt st. is to draw lines

2x+3y=6------> y=2-(2/3)x and
3r+2s=6 OR 3x+2y=6--------->y=3-(3/2)x

On the graph you will see that these two lines cross in one point, when x (which is r)=2; and y (which is s)=1. All other points of 3r+2s=6 do not lie in region R. Thus inconslusive, cuz we do not know if the coordinates (2,1) or else.

2nd- suff.

Once we know exact coordinates of point, we can defenetely say if it is in region R or not. Any point has only one set of coordinates (x,y).
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