Question

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

Answer 1

Answer:

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Answer 2

Answer:

$\boxed{The \;required \;value \;of \; k \; is \boxed{2}}$

Step-by-step explanation:

The Given Equations are,

$\bigstar$ 3x - y + 8 = 0

     and

$\bigstar$ 6x - ky = -16 $\implies$ 6x- ky+ 16 =0

It is mentioned in the question that they represent intersecting lines.

The condition for the lines to intersect is,

$\dfrac{a1}{a2} = \dfrac{b1}{b2} = \dfrac{c1}{c2}$

Here,

a1 = 3

a2 = 6

b1 = -1

b2= -k

c1 = 8

c2 = 16

∴

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

$\implies$ $\dfrac{1}{2} = \dfrac{1}{k} = \dfrac{1}{2}$

So,

$\dfrac{1}{2} = \dfrac{1}{k}$

∴ 1× k = 2×1

$\implies$ $\underline{\underline{{k = 2}}}}$