Question

for what value of K do the equation 3x-y+8=0, 6x-ky=-16 represent co-incident lines

,​

Answer 1

Answer:

-2

Step-by-step explanation:

Co-incident lines mean that the equations have infinite solutions.

For infinite solutions, a1/a2 = b1/b2 = c1/c2.

First equation ---> 3x - y + 8 = 0

Second equation ---> 6x - ky = -16

=> 6x - ky + 16 = 0

a1 = 3            a2 = 6

b1 = -1           b2 = k

c1 = 8            c2 = 16

So, a1/a2 = b1/b2 = c1/c2

=> 3/6 = -1/k = 8/16

=> 1/2 = -1/k = 1/2

=> 1/2 = -1/k

∴ k = 2*-1 => -2         (Cross multiplication)

Thus, k's value should be -2 for 3x - y + 8=0 and 6x - ky= -16 to be coincident lines/have infinite solutions.