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

Condition for coincident lines is -

a₁/a₂ = b₁/b₂ = c₁/c₂ …(i)

Given lines, 3x - y + 8 = 0

and 6x - ky + 16 = 0;

Comparing with ax + by + c = 0;

Here, a₁ = 3, b₁ = - 1, c₁ = 8; a₂ = 6, b₂ = - k, c₂ = 16;

and

From Eq. (i),

So, k = 2