Question

for what value of k in 3x -y+8=0 and 6x-ky = -16 represent coincident lines?​

Answer 1

Answer:

k will have the value -2.

Since they are coincident equations, they will have a common point.

ie, 3x-y+8 = 2(3x + (k/2)y +8)

Since y terms are equal, -1 = k/2

k = -2

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Answer 2

$\bf\huge\underline{Question}$

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

$\bf\huge\underline{Solution}$

Given equations of lines are

3x - y + 8 = 0

6x - ky + 16 = 0

Here, ${a_1}$ = 3, ${b_1}$ = 1, ${c_1}$ = 8

and ${a_2}$ = 6, ${b_2}$ = -k, ${c_2}$ = 16

Since, condition for coincident lines is

$\dfrac{a_1}{a_2}$ = $\dfrac{b_1}{b_2}$ = $\dfrac{c_1}{c_2}$

∴ $\dfrac{3}{6}$ = $\dfrac{-1}{-k}$ = $\dfrac{8}{16}$ => $\dfrac{1}{k}$ = $\dfrac{1}{2}$

∴ k = 2