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# Co-ordinate

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Senior Manager
Joined: 16 Feb 2011
Posts: 259
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Kudos [?]: 163 [0], given: 9

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31 Jul 2011, 21:55
A given line L has an equation 3x+4y=5. Which of the following is the equation of line
which doesnot intersect the above line?

1) 4x+3y=5
2) 3x+4y=10
3) 3x+5y=5
4) 3x+5y=3
5) 3x-4y=5

Can anyone pls help me understand a simplest way to solve such questions..
I will share the answer after few explanations..
Manager
Status: Trying to survive
Joined: 29 Jun 2011
Posts: 183
GMAt Status: Quant section
Concentration: Finance, Real Estate
Schools: WBS (D)
GMAT Date: 12-30-2011
GPA: 3.2
Followers: 11

Kudos [?]: 110 [0], given: 94

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01 Aug 2011, 11:55
hello
i haven't start geometry yet but i can guess that it is 2. 3x+4y=10
my point of view is
3x+4y=5 so y=-3/4 x + 5/4
and 3x+4y=10 so y=-3/4 x + 10/4
they have the same Tendency so they have to be parallel
(if two lines have the same Tendency the have to parallel )
p.s I'm not sure if my solving is right
regards

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How can i lose my faith in life's fairness when i know that the dreams of those who sleep on the feathers are not more beautiful than the dreams of those who sleep on the ground? - Jubran Khaleel Jubran

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01 Aug 2011, 23:05
1
KUDOS
Expert's post
DeeptiM wrote:
A given line L has an equation 3x+4y=5. Which of the following is the equation of line
which doesnot intersect the above line?

1) 4x+3y=5
2) 3x+4y=10
3) 3x+5y=5
4) 3x+5y=3
5) 3x-4y=5

Can anyone pls help me understand a simplest way to solve such questions..
I will share the answer after few explanations..

The only way 2 lines lying on the xy axis will not intersect is if they are distinct parallel lines.

Say, the equation of 2 lines is:
ax + by + c = 0
mx + ny + p = 0

These two lines intersect in a single point if:
$$\frac{a}{m} \neq \frac{b}{n}$$

These two lines are distinct and parallel if:
$$\frac{a}{m} = \frac{b}{n} \neq \frac{c}{p}$$

They are the same line if:
$$\frac{a}{m} = \frac{b}{n} = \frac{c}{p}$$

Since you want to find parallel distinct lines i.e. no point of intersection, $$\frac{a}{m} = \frac{b}{n} \neq \frac{c}{p}$$ should hold.
given: 3x+4y=5
parallel: 3x+4y=10
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Senior Manager
Joined: 16 Feb 2011
Posts: 259
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Kudos [?]: 163 [0], given: 9

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02 Aug 2011, 03:17
VeritasPrepKarishma wrote:
DeeptiM wrote:
A given line L has an equation 3x+4y=5. Which of the following is the equation of line
which doesnot intersect the above line?

1) 4x+3y=5
2) 3x+4y=10
3) 3x+5y=5
4) 3x+5y=3
5) 3x-4y=5

Can anyone pls help me understand a simplest way to solve such questions..
I will share the answer after few explanations..

The only way 2 lines lying on the xy axis will not intersect is if they are distinct parallel lines.

Say, the equation of 2 lines is:
ax + by + c = 0
mx + ny + p = 0

These two lines intersect in a single point if:
$$\frac{a}{m} \neq \frac{b}{n}$$

These two lines are distinct and parallel if:
$$\frac{a}{m} = \frac{b}{n} \neq \frac{c}{p}$$

They are the same line if:
$$\frac{a}{m} = \frac{b}{n} = \frac{c}{p}$$

Since you want to find parallel distinct lines i.e. no point of intersection, $$\frac{a}{m} = \frac{b}{n} \neq \frac{c}{p}$$ should hold.
given: 3x+4y=5
parallel: 3x+4y=10

What if the question is to find a point at which the line intersect 3x+4y=5?
Manager
Status: Trying to survive
Joined: 29 Jun 2011
Posts: 183
GMAt Status: Quant section
Concentration: Finance, Real Estate
Schools: WBS (D)
GMAT Date: 12-30-2011
GPA: 3.2
Followers: 11

Kudos [?]: 110 [0], given: 94

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02 Aug 2011, 06:11
you solve for the two functions and you get the intersecting point (x,y)
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How can i lose my faith in life's fairness when i know that the dreams of those who sleep on the feathers are not more beautiful than the dreams of those who sleep on the ground? - Jubran Khaleel Jubran

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11 Feb 2016, 11:29
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Co-ordinate   [#permalink] 11 Feb 2016, 11:29
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