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# In the xy-plane, does the line w/ equation y=3x+2 contain

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

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01 Jan 2007, 12:29
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In the xy-plane, does the line w/ 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

This question has been posted before but I am still confused on the explanation.
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01 Jan 2007, 12:44

for (r,s) to be on the line y=3x+2 it is necessary and sufficient that 2=3r+2 => 3r+2-s=0

from st1 we know that either (3r+2-s)=0 or (4r+9-s)=0 so it is insufficient.
from st2 we know that either (3r+2-s)=0 or (4r-6-s)=0 so it is insufficient.

taking them together is sufficient. it can't be that both 4r+9-s=0 and 4r-6-s=0. so it must be that 3r+2-s=0

hence C.
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01 Jan 2007, 12:50
Thanks Hobbit... Just figured out the explanation, right after I posted the question.
Was confused about whether s=3r+2 and y=3x+2 are the same line
01 Jan 2007, 12:50
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