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

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Director
Joined: 11 Sep 2006
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In the xy plane, does the line with equation y = 3x+2 [#permalink]  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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VP
Joined: 25 Jun 2006
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C.

if u combine them, u get 3r + 2 = s. either one alone is not Suff.
Director
Joined: 11 Sep 2006
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OA was C. Don't know why that threw me - not a toughie, as such...ah well.
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Intern
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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...

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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...

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.
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