Question

Assertion :If $kx-y-2=0$ and $6x-2y-3=0$ are inconsistent, then $k=3$ Reason: $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$ are inconsistent if $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Let $kx-y-2=0......\left(1\right)$
$6x-2y-3=0......\left(2\right)$
For the equation to be inconsistent
$\Rightarrow \frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$
$\Rightarrow \frac{k}{6}=\frac{-1}{-2}\ne \frac{-2}{-3}$
$\therefore k=3$
Therefore the Assertion is correct.
Clearly, the Reason is correct.
Since both the Assertion and Reason are correct and Reason is a correct explanation of Assertion.
The correct answer is A.