Math, asked by simrandhanna, 1 month ago

what value of k do the equations 3x-y+18=0 and 6x-ky=-16 represent coincident lines​ please kaevaa dooo

Answers

Answered by amitnrw
3

Given :  3x-y+ 8=0 and 6x-ky=-16 represent coincident lines

To Find : Value of k

Solution:

Two lines

a₁x  + b₁y  + c₁ = 0

a₂x  + b₂y  + c₂ = 0

parallel  if  a₁/a₂  = b₁/b₂  

Coincident if a₁/a₂  = b₁/b₂  =  c₁ / c₂

Intersect at a point  if a₁/a₂ ≠ b₁/b₂  

3x-y+ 8=0

6x-ky=-16

=> 6x - ky + 16 = 0

=> 3/6  = -1/-k  =  8/16

=> 1/2 = 1/k  = 1/2

=> K = 2

if we take 3x-y+ 18=0  as given in question

Then these lines can not be coincident

as  1/2  ≠ 18/16

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Answered by RvChaudharY50
2

Given :- what value of k do the equations 3x-y+18=0 and 6x-ky=-16 represent coincident lines ?

Answer :-

we know that,

  • when two lines have the same slope and the same y - intercept, the lines are coincident.

so,

→ 3x - y + 18 = 0

→ 3x + 18 = y

comparing with y = mx + c

→ slope = 3

similarly,

→ 6x - ky = (-16)

→ 6x + 16 = ky

→ (6/k)x + (16/k) = y

comparing with y = mx + c

→ slope = (6/k)

then,

→ 6/k = 3

→ k = 6/3 = 2 (Ans.)

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