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

1.	For what value of k, do the equations 3x - y + 8 = 0 and 6x - ky + 16 = 0 represent coincident lines? A. 1/2B. -1/2C. 2 D. - 2
Answer» C. 2 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), 3/6 = 1/k = 8/16 1/k = 1/2 So, k = 2

For what value of k, do the equations 3x - y + 8 = 0 and 6x - ky + 16 = 0 represent coincident lines? A. 1/2B. -1/2C. 2 D. - 2

Answer»

C. 2

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), 3/6 = 1/k = 8/16

1/k = 1/2

So, k = 2