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Re: In the XY plane, does the line with equation y=3x+2 [#permalink]
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.

Re: In the XY plane, does the line with equation y=3x+2 [#permalink]
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

In the XY plane, does the line with equation y=3x+2 [#permalink]
25 Nov 2014, 11:28

(Just so I get the whole picture) Say, instead of the bold parts in (3r+2-s)(4r+9-s)=0 and (4r-6-s)(3r+2-s)=0, there are 2 slightly unrelated terms like 5r-3-s and 2r+7-s.They would remain to be possibilities of the equation and E would be the right choice, right? Sorry if I am complicating things.

Last edited by deeuk on 26 Nov 2014, 10:36, edited 1 time in total.

Re: In the XY plane, does the line with equation y=3x+2 [#permalink]
26 Nov 2014, 04:46

Expert's post

deeuk wrote:

(Just so I get the whole picture) Say, instead of the bold parts in (3r+2-s)(4r+9-s)=0 and (4r-6-s)(3r+2-s)=0, there were 2 slightly unrelated terms like 5r-3-s and 2r+7-s, they would remain to be possibilities of the equation and E would be the right choice, right? Sorry if I am complicating things.

Yes, in this case the answer would be E. _________________

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