In xy plane, does the line with equation y=3x+2 contain : DS Archive
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In xy plane, does the line with equation y=3x+2 contain

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In xy plane, does the line with equation y=3x+2 contain [#permalink]

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New post 16 Sep 2006, 17:18
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In xy plane, does the line with equation y=3x+2 contain point (r,s)?

1) (3r + 2 - s)(4s + 9 - s) = 0

2) (4r - 6 - s)(3r + 2 - s) = 0

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Last edited by MBAlad on 17 Sep 2006, 04:55, edited 1 time in total.
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New post 17 Sep 2006, 04:20
MBAlad wrote:
In xy plane, does the line with equation y=3x+2 contain point (r,s)?

1) (3r + 2 - s)(4s + 9 - s) = 0

2) (4r - 6 - s)(3r + 2 - 5) = 0



1. SUFFICIENT:,
3r +2 = s
3x +2 = y
are essentially the same equation so any (r;s) solves the stem equation

2. INSUFFICIENT

s = 4r-6 only crosses y = 3x+2 at one point (9;26)


Answer: A
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New post 17 Sep 2006, 04:24
Can you also tell me how you calculated the points at which the lines intersect?
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New post 17 Sep 2006, 04:44
MBAlad wrote:
In xy plane, does the line with equation y=3x+2 contain point (r,s)?

1) (3r + 2 - s)(4s + 9 - s) = 0

2) (4r - 6 - s)(3r + 2 - 5) = 0


Hey MBAlad, i guess the second condition must be (4r-6-s)(3r+2-s)=0
Then only the answer will be C

From 1 : (3r+2-s)(4s+9-s)=0 means

(3r+2-s) = 0 or ((4s+9-s) = 0

If (3r+2-s) = 0 then the line passes through (r,s).
If we consider the second case we can't determine.

Similarly From 2: also we get the same answer.

Combining both we can conclude that 1 and 2 will be equal to 0 provided only (3r+2-s) = 0 and hence the answer is C.

But i think the correction must be there in stat 2 as i mentioned earlier
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Last edited by cicerone on 25 Sep 2008, 00:09, edited 1 time in total.
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New post 17 Sep 2006, 04:56
Yes sorry, have edited the original.

Would you mind expanding on your reasoning and say how you know the lines intersect and how you calculate this?

Thanks
  [#permalink] 17 Sep 2006, 04:56
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