Choose the correct answer from the given four options:
For what value of \( k \), do the equations \( 3 x-y+8=0 \) and \( 6 x-k y=-16 \) represent coincident lines?
(A) \( \frac{1}{2} \)
(B) \( -\frac{1}{2} \)
(C) 2
(D) \( -2 \)
Given:
The pair of equations \( 3 x-y+8=0 \) and \( 6 x-k y=-16 \) are coincident lines.
To do:
We have to find the correct option.
Solution:
We know that,
The condition for coincident lines is,
$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
\( 3 x-y+8=0 \) and \( 6 x-k y=-16 \)
Here,
$a_1=3, b_1=-1, c_1=8$
$a_2=6, b_2=-k, c_2=16$
Therefore,
$\frac{3}{6}=\frac{-1}{-k}=\frac{8}{16}$
$\frac{1}{k}=\frac{1}{2}$
$k=2$
The value of $k$ is $2$.
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