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Question

In the pair of equations a1x+b1y+c1=0 and a2x+b2y+c2=0,

a1a2=b1b2c1c2

Statement 1 : This is an inconsistent pair of linear equations.

Statement 2 : There exists infinitely many solutions.

Statement 3 : The lines representing these linese are parallel.

Which of the above statements is/are true?


A

S1 only

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B

S1 and S2

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C

S1 and S3

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D

S2 only

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Solution

The correct option is C

S1 and S3


In the pair of equations a1x+b1y+c1=0 and a2x+b2y+c2=0,

if a1a2=b1b2c1c2, then the lines representing these equations are parallel.

Hence, there will be no solution and the pair of equations will be inconsistent.

Statements 1 and 3 are correct.


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