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

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Re: In the XY plane, does the line with equation y=3x+2 [#permalink] New post 31 Aug 2013, 05:13
Expert's post
danzig wrote:
Bunuel,

In statement (1), you have said that we have these possibilities:
(3r + 2 - s) = 0 OR (4r + 9 - s) = 0 OR both.

But, when we have something like this:
(x + 3)(x+5) = 0

In this case, there are only two possibilities, right? (x+3)=0 OR (x+5)=0.
Both cannot be zero at the same time because "x" represents a single and unique value.
Please confirm.


Yes.

(3r + 2 - s) = 0 and (4r + 9 - s) = 0 can both be true, for r=-7 and s=-19.

But for (x+3)=0 and (x+5)=0 both cannot be true simultaneously. Either x=-3 or x=-5.

Hope it's clear.
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Re: In the XY plane, does the line with equation y=3x+2 [#permalink] New post 07 Jun 2014, 11:40
could we also think of it as:

the following two equations define two non-identical hyperbola.
1) (3r+2-s) (4r+9-s)=0
2) (4r-6-s) (3r+2-s)=0

each equation represents a set of points on different hyperbola
since the question states that (r,s) is one point,
it must be a single intersection of the two hyperbola which cannot be found without both equations.

therefore: you need both equations to define one point (r,s) and then you can easily solve for whether (r,s) satisfies the first equation y = 3x+2

would that reasoning also work?
Re: In the XY plane, does the line with equation y=3x+2   [#permalink] 07 Jun 2014, 11:40
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