find the value of k, if Kx +3y = K-3 and 12x + KY =K represent coincident line.
Answers
Therefore the value of k = 6.
Given : two equations ; kx + 3y = k - 3 and 12x + ky = k represent coincident lines.
To find : The value of k.
solution : we know, two lines a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 represent coincident lines.
only if a₂/a₁ = b₂/b₁ = c₂/c₁
⇒12/k = k/3 = k/(k - 3)
12/k = k/3
⇒12 × 3 = k²
⇒k² = 36 = 6²
⇒k = 6 , -6 ..........(1)
again, k/3 = k/(k - 3)
⇒k(k - 3) = 3k
⇒k² - 3k = 3k
⇒k² - 6k = 0
⇒k(k - 6) = 0
⇒k = 0, 6 ...........(2)
taking common values of k from equations (1) and (2) we get,
k = 6
Therefore the value of k = 6
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Answer:
k=6
Step-by-step explanation:
Answer proved above :)