Question

The value of k for which the pair of linear equations $4x+6y-1=0$ and $2x+ky-7=0$
represents parallel lines is

• A. $k=3$
• B. $k=2$
• C. $k=4$
• D. $k=-2$

Answer 1

The correct option is A $k=3$

The pair of linear equations represents parallel lines if:

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

For the given pair of equation $4x+6y-1=0and2x+ky-7=0;$

$\frac{a_1}{a_2}=\frac{4}{2}=2$

$\frac{b_1}{c_2}=\frac{6}{k}$

$\frac{c_1}{c_2}=\frac{-1}{-7}=\frac{1}{7}$

For $\frac{a_1}{a_2}=\frac{b_1}{b_2}⟶k=3$

The pair of linear equations represents parallel lines for $k=3$.