Question

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

Answer 1

$3x - y + 8 = 0 \: and \: \\ 6x - ky = - 16$

here, Let's take x as 2

then,

$3(2) - y + 8 = 0 \: and \: \\ 6(2) - ky = - 16$

$6 - y + 8 = 0 \: and \: \\ 12 - ky = 16$

$y = 8 - 6 = 2 \: and \\ ky = 16 - 12$

NOW,

$y = 2 \: and \: \\ ky = 4$

NOW,

$y = 2 \: and \: 4$

$k = \frac{4}{2}$

$k = 2$

THEREFORE, the value of K = 2

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Answer 2

Answer:

$\boxed{\text{\underline{k=2}}}$  k = 2

Explanation:

given : 3x - y + 8 = 0 and 6x + ky = - 16

a₁=3, b₁=-1, c₁=8

a₂=6, b₂=k, c₂=16

to find: value of k

solution: coincident lines, means infinitely many solutions

$\frac{a_{1} }{a_{2} } =\frac{b_{1} }{b_{2} } =\frac{c_{1} }{c_{2} }$

put the values

$\frac{3}{6} =\frac{1}{k} = \frac{8}{16}$

solve for k

$\frac{1}{k} = \frac{8}{16}$

cross-multiplication

$8k=16$

$k=\frac{16}{8}$

$k=2$

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