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

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k=1

k=2

k=3

k=4

answer is B.

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Detailed Solution

Given equations are

3 x − y + 8 = 0

and

6 x − k y = − 16

.
We know that there are an infinite number of solutions to the pair of linear equations or they are said to be coincident lines graphically, if

a 1 a 2 = b 1 b 2 = c 1 c 2

.
On comparing the above equations with

a 1 x + b 1 y + c 1 = 0

and

a 2 x + b 2 y + c 2 = 0

, we get

a 1 = 3, b 1 = − 1, c 1 = 8

and

a 2 = 6, b 2 = − k, c 2 = 16.

Let us substitute the above values in the condition

a 1 a 2 = b 1 b 2 = c 1 c 2

. We get,

36 = − 1 − k = 816 ⇒ 12 = 1 k = 12

By observing the above ratios, we get the value of k = 2.
The value of k for which the given system of equations are coincident is 2.
The correct option is (2).

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