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Math Expert V
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A given line L has an equation 3x+4y=5. Which of the following is the  [#permalink]

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A given line L has an equation 3x+4y=5. Which of the following is the equation of line which does not intersect the above line?

(A) 4x + 3y = 5
(B) 3x + 4y = 10
(C) 3x + 5y = 5
(D) 3x + 5y = 3
(E) 3x – 4y = 5

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A given line L has an equation 3x+4y=5. Which of the following is the  [#permalink]

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At the point of intersection of 2 given lines , the 2 lines will share a point and thus will have the same value of x and y coordinates .
3x+4y=5 --- equation 1
To find an equation of line which does not intersect above line , we can substitute the value of x or y from one line in other and solve it.
2 lines are parallel if
a1/a2 = b1/b2 ≠ c1/c2
Alternatively , we can solve it quickly by looking at the answer options .
Comparing the original line with option B
3x+4y = 10 -- equation 2
From equations 1 and 2 , we get
5=10
which is not possible
Hence our answer is 3x + 4y = 10
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Re: A given line L has an equation 3x+4y=5. Which of the following is the  [#permalink]

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Bunuel wrote:
A given line L has an equation 3x+4y=5. Which of the following is the equation of line which does not intersect the above line?

(A) 4x + 3y = 5
(B) 3x + 4y = 10
(C) 3x + 5y = 5
(D) 3x + 5y = 3
(E) 3x – 4y = 5

any parallel line cant intersect , so B is the answer.
Intern  Joined: 13 Jan 2011
Posts: 3
Re: A given line L has an equation 3x+4y=5. Which of the following is the  [#permalink]

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Basically a question of whether we can solve for x,y using the given equation (3x + 4y = 5) and any one of the options. The answer will be the one which doesnt give us a solution for x,y.

Viewing the options, it's clear that B will never give us the solution for x,y and hence B is the answer
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4003
A given line L has an equation 3x+4y=5. Which of the following is the  [#permalink]

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Bunuel wrote:
A given line L has an equation 3x+4y=5. Which of the following is the equation of line which does not intersect the above line?

(A) 4x + 3y = 5
(B) 3x + 4y = 10
(C) 3x + 5y = 5
(D) 3x + 5y = 3
(E) 3x – 4y = 5

IMPORTANT: If a line intersects another line, then the coordinates of the point of intersection will satisfy the equations for BOTH lines.

Notice that line L tells us that 3x + 4y = 5. That is, the coordinates of ANY point on line L will satisfy the equation 3x + 4y = 5
The equation for answer choice B is 3x + 4y = 10. That is, the coordinates of ANY point on line B will satisfy the equation 3x + 4y = 10
As you can see, it's impossible for a set of coordinates to satisfy the equation 3x + 4y = 5 AND the equation 3x + 4y = 10
In one case, the sum of 3x and 4y is 5, and in the other case, the sum of 3x and 4y is 10. We can't satisfy both equations at the same time.
So, those two lines CANNOT share a common point.

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A given line L has an equation 3x+4y=5. Which of the following is the  [#permalink]

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parallel lines have same slope.

3x+4y-5= 0 ...equation of the line in the form ax+bY-C , slope =- a/b = -3/4

given line slope is -3/4 , from the given choices only line B satisfy the condition slope = -3/4
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Re: A given line L has an equation 3x+4y=5. Which of the following is the  [#permalink]

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if slope of two lines are equal then both lines are parallel to each other.

slope of first line is -3/4, we have to find out equation which has same slope as -3/4. Only option B satisfies. Re: A given line L has an equation 3x+4y=5. Which of the following is the   [#permalink] 28 Jan 2019, 17:30
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