Question

In the pair of equations $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$,

$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

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
• B. S1 and S2
• C. S1 and S3
• D. S2 only

Answer 1

The correct option is C

S1 and S3

In the pair of equations $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$,

if $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$, then the lines representing these equations are parallel.

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

$\therefore$ Statements 1 and 3 are correct.