**Question:**

The value of k for which the pair of linear equation 4x + 6y − 1 = 0 and 2x + ky − 7 = 0 represent parallel lines is

(a) k = 3

(b) k = 2

(c) k = 4

(d) k = −2

**Solution:**

Given that the pair of linear equation $4 x+6 y-1=0$ and $2 x+k y-7=0$

$a_{1}=4, b_{1}=6, c_{1}=-(-1)=1$

$a_{2}=2, b_{2}=k, c_{2}=-(-7)=7$

It is given that the pair of equations represent parallel lines.

$\therefore \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$

$\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}$

$\Rightarrow \frac{4}{2}=\frac{6}{k}$

$\Rightarrow k=3$

Hence the option (a) is correct.