Question

Assertion (A)
The system of equations $2x+3y+5=0\mathrm{and}4\mathrm{x}+\mathrm{ky}+7=0$ is inconsistent when k = 6.
Reason (R)
The system of equations $a_{1}x+b_{1}y+c_1=0\mathrm{and}{\mathrm{a}}_2\mathrm{x}+{\mathrm{b}}_2\mathrm{y}+{\mathrm{c}}_2=0$ is inconsistent when $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}.$
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

Answer 1

Option (a) is correct.
Reason (R) is clearly true.
For the given system to be inconsistent, we must have,
$\frac{a}{b}=\frac{c}{d}\ne \frac{e}{f}$
Also, $\frac{2}{4}=\frac{3}{k}\ne \frac{5}{7}\Rightarrow k=6$
So, Assertion (A) is true and, clearly, Reason (R) is a correct explanation of Assertion (A).