Question

If the equations 3x – y + 8 = 0 and 6x – ky = - 16 represent coincident lines. Find the value of 'k'.

Answer 1

Condition for coincident lines is
$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$.... (i)
Given lines:
3x – y + 8 = 0
6x – ky + 16 = 0
Here,
$a_1=3,b_1=-1,c_1=8$
$a_2=6,b_2=-k,c_2=16$
from Eq. (i)
$\frac{3}{6}=\frac{-1}{-k}=\frac{8}{16}$
$\Rightarrow \frac{1}{k}=\frac{1}{2}\therefore k=2$