Question

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

Options

• `1/2`

• `-1/2`

• 2

• –2

Answer 1

2

Explanation:

Given equations of lines are 3x – y + 8 = 0 and 6x – ky + 16 = 0

Here, a₁ = 3

b₁ = –1

c₁ = 8

And a₂ = 6

b₂ = –k

c₂ = 16

Since, condition for coincident lines is

`a_1/a_2 = b_1/b_2 = c_1/c_2`

∴ `3/6 = (-1)/(-k) = 8/16`

⇒ `1/k = 1/2`

∴ k = 2