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