Question

If the lines $kx-2y-1=0$ and $6x-4y-m=0$ are identical (coincident) lines, then the values of $k$ and $m$ are:

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

Answer 1

The correct option is A

$k=3,m=2$

Explanation for the correct option

Given lines $kx-2y-1=0$ and $6x-4y-m=0$ are coincident lines,

We know that if lines $a_{1}x+b_{1}y+c_1=0,a_{2}x+b_{2}y+c_2=0$ are coincident then $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

For the given lines, $\frac{k}{6}=\frac{-2}{-4}=\frac{-1}{-m}$

Let, $\frac{k}{6}=\frac{1}{2}$, so, $k=3$

Similarly, $\frac{1}{m}=\frac{1}{2}$, so, $m=2$

Therefore, option (A) i.e. $k=3,m=2$ is the correct answer.