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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]

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New post 31 Aug 2013, 06:13
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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]

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New post 07 Jun 2014, 12:40
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?
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In the XY plane, does the line with equation y=3x+2 [#permalink]

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New post 25 Nov 2014, 12:28
(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, 11:36, edited 1 time in total.
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Re: In the XY plane, does the line with equation y=3x+2 [#permalink]

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New post 26 Nov 2014, 05:46
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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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In the xy plane, does the line y=3x+2 contain the point (r,s)? i) (3r+ [#permalink]

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New post 01 Aug 2015, 23:38
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In the xy plane, does the line y=3x+2 contain the point (r,s)?
i) (3r+2-s)(4r+9-s)=0
ii) (4r-6-s)(3r+2-s)=0
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Re: In the xy plane, does the line y=3x+2 contain the point (r,s)? i) (3r+ [#permalink]

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New post 02 Aug 2015, 03:24
visram04 wrote:
In the xy plane, does the line y=3x+2 contain the point (r,s)?
i) (3r+2-s)(4r+9-s)=0
ii) (4r-6-s)(3r+2-s)=0



Question Stem: If Point (r,s) lies on the line y =3x+2, then the point should satisfy the equation, i.e., s=3r+2

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

3r+2 = s or 4r+9 =s
We dont have unique solution. Hence not sufficient

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


4r-6 = s or 3r+2 = s
We dont have unique solution. Hence not sufficient

Combined:

Combining we get s = 3r+2 --> which is required to prove from the question stem.
Hence sufficient.
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In the XY plane, does the line with equation y=3x+2 [#permalink]

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New post 22 Mar 2016, 04:32
gaurav2k101 wrote:
In the xy-plane , does the line with equation y=3x+2 contains the point(r,s)?

(1) (3r+2-s)(4r+9-s)=0
(2) (4r-6-s)(3r+2-s)=0



I did it differently, but it could be totally wrong. It would be good if someone can check it. Bunuel I would highly appreciate it if you check it.

I substituted 0 for r for both statements,

(1) (3(0)+2-s)(4(0)+9-s)=0 so that s=2 (which is on the line) or 9 (which is not on the line)

(2) (4(0)-6-s)(3(0)+2-s)=0 so that s=6 (which is not on the line) or 2 (which is on the line)

Alone statement 1 and 2 are insufficient since they could be either 1 of 2 values, but together they prove that s=2, so the answer is C.
In the XY plane, does the line with equation y=3x+2   [#permalink] 22 Mar 2016, 04:32

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