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 $

AcademicMathematicsNCERTClass 10

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 $2$.

raja
Updated on 10-Oct-2022 13:27:12

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