Question

For what value of $k$, do the equations $3x-y+8=0$ and $6x-ky=-16$ represent coincident lines?

• A. $\frac{1}{2}$
• B. $-\frac{1}{2}$
• C. $2$
• D. $-2$

Answer 1

Answer: (C)

$2$

The equations are
$3x-y+8=0$
$6x-ky+16=0$
Here, $a_1=3,b_1=-1,c_1=8$
and $a_2=6,b_2=-k,c_2=16$
The equation will represent coincident lines only when they have infinite number of solutions.
$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
$\Rightarrow \frac{3}{6}=\frac{-1}{-k}=\frac{8}{16}$
Taking,
$\frac{3}{6}=\frac{-1}{-k}$
$\Rightarrow \frac{1}{2}=\frac{1}{k}$
$\Rightarrow k=2$

Taking,
$\frac{-1}{-k}=\frac{8}{16}$
$\Rightarrow \frac{1}{k}=\frac{1}{2}$
$\Rightarrow k=2$
So, the answer is $k=2$