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Question

Which of the following pair of lines are parallel to each other?

A
x+7y=6; 2x+14y=12
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B
5x+7y=12; 2x+14y=12
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C
x+2y=7; 3x+6y=28
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D
11x+2y=4; 3x+6y=10
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Solution

The correct option is C x+2y=7; 3x+6y=28
A pair of equations is said to form parallel lines if they have no solution.

Let two equations be a1x+b1y+c1=0 and a2x+b2y+c2=0.

Then, the condition for a pair of linear equations to be parallel:
a1a2=b1b2c1c2

For equations:
x+2y=7; 3x+6y=21
a1=1;b1=2;c1=7
a2=3;b2=6;c2=28

13=26728
13=1314

x+2y=7; 3x+6y=28 are parallel to each other.

For equations:
x+7y=6; 2x+14y=12
a1=1;b1=7;c1=6
a2=2;b2=14;c2=12

12=714612
12=12=12

x+2y=7; 3x+6y=28 are not parallel to each other.


For equations:
5x+7y=12; 2x+14y=12
a1=5;b1=7;c1=12
a2=2;b2=14;c2=12

52=7141212
521211

5x+7y=12; 2x+14y=12 are not parallel to each other.


For equations:
11x+2y=4; 3x+6y=10
a1=11;b1=2;c1=4
a2=3;b2=6;c2=10

113=26410
1131325

5x+7y=12; 2x+14y=12 are not parallel to each other.


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