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

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In the xy-plane, does the line with equation y=3x+2 contain [#permalink]  06 Jul 2008, 08:24
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In the xy-plane, does the line with equation y=3x+2 contain (r,s)?

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

no clue!!
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Re: DS- Line equation [#permalink]  06 Jul 2008, 09:44
In the xy-plane, does the line with equation y=3x+2 contain (r,s)?

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

S1. Tells you that (3r+2-s) = 0; s = 3r + 2
S2. Tells you that (3r+2-s) = 0; s = 3r + 2

so (3r+2-s) is the common value in both the equations and this satisfies the equation y = 3x + 2

IMO C

Last edited by x97agarwal on 06 Jul 2008, 21:07, edited 1 time in total.
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Re: DS- Line equation [#permalink]  06 Jul 2008, 09:59
kapilnegi wrote:
In the xy-plane, does the line with equation y=3x+2 contain (r,s)?

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

no clue!!

If line y=3x+2 passes thru (r,s) then s = 3r+2
or s- 3r-2 =0
or 3r+2-s =0

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

D
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Re: DS- Line equation [#permalink]  06 Jul 2008, 13:38
I think C.

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

which gives 3r+2-s=0 or s=3r+2
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Re: DS- Line equation [#permalink]  06 Jul 2008, 19:00
x97agarwal wrote:
In the xy-plane, does the line with equation y=3x+2 contain (r,s)?

1. (3r+2-s)(4r+9-s)=0; = 13r^2 +35 r - 7rs + 8r - 11s + s^2 + 36
2. (4r-6-s)(3r+2-s)=0

S1. Tells you that (3r+2-s) = 0; s = 3r + 2
S2. Tells you that (3r+2-s) = 0; s = 3r + 2

so (3r+2-s) is the common value in both the equations and this satisfies the equation y = 3x + 2

IMO C

X97, Stat1 and 2 give the same info. I dont understand why C? Pls explain.
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Re: DS- Line equation [#permalink]  06 Jul 2008, 19:35
when x*y = 0

the information we have is either x=0 OR y=0

statement 1 gives either (3r+2-s) = 0 OR (4r+9-s)=0. so the answer of our question could be either "yes" or "no"....

Similiar logic for statement 2.

thats why C is the answer.

its something like this

Question x = ?
1. x=3 or 4
2. x=3 or 5 Option C
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Re: DS- Line equation [#permalink]  06 Jul 2008, 21:13
1
KUDOS
goalsnr wrote:
x97agarwal wrote:
In the xy-plane, does the line with equation y=3x+2 contain (r,s)?

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

S1. Tells you that (3r+2-s) = 0; s = 3r + 2
S2. Tells you that (3r+2-s) = 0; s = 3r + 2

so (3r+2-s) is the common value in both the equations and this satisfies the equation y = 3x + 2

IMO C

X97, Stat1 and 2 give the same info. I dont understand why C? Pls explain.

From S1. (3r+2-s) = 0 or (4r+9-s)=0
S2. (4r-6-s) = 0 or (3r+2-s)=0
Exaple: If xy = 0 then either x = 0 or y = 0 or x and y both = 0
Similarily:
Lets assume that (3r+2-s) is not = 0 and (4r-6-s) = 0 and (4r+9-s)=0
Now equate both these equations, (4r-6-s) = (4r+9-s), you will get 15 = 0, which is not possible

The only way the equation can have a solution is if (3r+2-s) = 0
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Re: DS- Line equation [#permalink]  07 Jul 2008, 05:19
x97agarwal wrote:
goalsnr wrote:
x97agarwal wrote:
In the xy-plane, does the line with equation y=3x+2 contain (r,s)?

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

S1. Tells you that (3r+2-s) = 0; s = 3r + 2
S2. Tells you that (3r+2-s) = 0; s = 3r + 2

so (3r+2-s) is the common value in both the equations and this satisfies the equation y = 3x + 2

IMO C

X97, Stat1 and 2 give the same info. I dont understand why C? Pls explain.

From S1. (3r+2-s) = 0 or (4r+9-s)=0
S2. (4r-6-s) = 0 or (3r+2-s)=0
Exaple: If xy = 0 then either x = 0 or y = 0 or x and y both = 0
Similarily:
Lets assume that (3r+2-s) is not = 0 and (4r-6-s) = 0 and (4r+9-s)=0
Now equate both these equations, (4r-6-s) = (4r+9-s), you will get 15 = 0, which is not possible

The only way the equation can have a solution is if (3r+2-s) = 0

Ah...Get it. 4 years of engineering were just a waste of time

Thanks. Kudos.
Re: DS- Line equation   [#permalink] 07 Jul 2008, 05:19
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