Les
Find the value of k, if the pair of linear equations 2x - 3y = 8 and
2 (k - 4 ) x-ky = k + 3 are inconsistent.
Answers
Given : pair of linear equations 2x-3Y =8 and 2 (K - 4) x - ky = K + 3 are inconsistent
To find : Value of K
Solution:
2x - 3Y = 8
2 (K - 4) x - ky = K + 3
Pair of lines
a₁x + b₁y = c₁ &
a₂x + b₂y = c₂
is inconsistent if
a₁/a₂ = b₁/b₂ ≠ c₁ /c₂
a₁ = 2 b₁ = -3 c₁ = 8
a₂ = 2(k - 4) b₂ = - k , c₂ = k + 3
2/2(k - 4) = -3/-k
=> k = 3k - 12
=> 2k = 12
=> k = 6
a₁/a₂ = b₁/b₂ = 2/2(6 - 4) = -3/-6 = 1/2
c₁ /c₂ = 8/k + 3 ≠ 1/2
=> 16 ≠ k + 3
=> k ≠ 13
hence k = 6 is the value
for which pair of linear equations 2x-3Y =8 and 2 (K - 4) x - ky = K + 3 are inconsistent
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