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In the xy plane, does the line with equation y = 3x+2

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Director
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In the xy plane, does the line with equation y = 3x+2 [#permalink] New post 02 Nov 2006, 19:06
In the xy plane, does the line with equation y = 3x+2 contain the point (r,s)?

1)(3r+2-s)(4r+9-s) = 0
2)(4r-6-s)(3r+2-s) = 0
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 [#permalink] New post 02 Nov 2006, 19:38
C.


if u combine them, u get 3r + 2 = s. either one alone is not Suff.
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 [#permalink] New post 03 Nov 2006, 22:43
OA was C. Don't know why that threw me - not a toughie, as such...ah well.
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 [#permalink] New post 03 Nov 2006, 23:04
Sorry if this is dumb or obvious, but I'm just starting out and need a little more elaboration on why they aren't sufficient alone...


thanks in advance
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 [#permalink] New post 04 Nov 2006, 02:55
claytont wrote:
Sorry if this is dumb or obvious, but I'm just starting out and need a little more elaboration on why they aren't sufficient alone...


thanks in advance


y = 3x+2
<=> 3x + 2 - y = 0 contain the point (r,s)?
=> 3r+2-s = 0 ? (A)

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

implies that
o 3r+2-s = 0 exactly (A)
or
o 4r+9-s = 0 : 1 point is shared with (A)

INSUFF

Start 1:
(4r-6-s)(3r+2-s) = 0

implies that
o 4r-6-s = 0 : 1 point is shared with (A)
or
o 3r+2-s = 0 exactly (A)

INSUFF

Both (1) & (2)

We have this system of equations :

o 4r+9-s = 0 or 3r+2-s = 0 (I)
AND
o 4r-6-s = 0 or 3r+2-s = 0 (II)

The "and" operand forces to look for an equation in (I) and (II) that guarantes both to be equal to 0. Hence, we have to choose 3r+2-s = 0.

SUFF.
  [#permalink] 04 Nov 2006, 02:55
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In the xy plane, does the line with equation y = 3x+2

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