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Question

Which of the following pairs of equations is inconsistent?

A
2x+3y=15;4x+7y=11
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B
4x+y=12;8x+2y=24
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C
x+2y=5;2x+4y=15
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D
11y+3x=1;5y+2x=7
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Solution

The correct option is C x+2y=5;2x+4y=15
A pair of linear equations in two variables is said to be inconsistent when:
a1a2=b1b2c1c2

Consider the equations given in option A.
2x+3y=15
4x+7y=11
Here, a1=2, b1=3 and c1=15
Also, a2=4, b2=7 and c2=11
Here, 2437
a1a2b1b2
Equations in option A have unique solution and are consistent.

Consider equations given in option B.
48=12=122412=12=12
a1a2=b1b2=c1c2
Equations in option B have infinite solutions and are consistent.

Consider equations given in option C.
12=24515
a1a2=b1b2c1c2
Equations in option C have no solution and are inconsistent.


Consider equations given in option D.
32115
a1a2b1b2
Equations in option D have a unique solution and are consistent.

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