Question

find the value of k, if the pair of linear equations 2x+3y=8 and 2(k-4)x-ky=k+3 are inconsistent​

Answer 1

Answer:

k = 3

Step-by-step explanation:

if the pair of linear eqns are inconsistent then ,

$a_{1} /a_{2} = b_{1} /b_{2} \neq c_{1} /c_{2}$

=> 2/(2k - 8) = 3/-k ≠ 8/(k+3)

Let's find the value of k by solving 2/(2k - 8) = 3/-k

=> 3(2k - 8) = -2k ( By cross multiplying....)

=> 6k - 24 = -2k

=> 8k = 24

=> k = 24/8 = 3

Let's verify the value of k in 3/-k ≠ 8/(k+3)

=> 3/(-3) ≠ 8/(3+3)

=> -1 ≠ 8/6

Hence the value of k = 3

Answer 2

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

=> 4k = 12

=> k = 3

a₁/a₂  = b₁/b₂  = 2/2(3 - 4)  = -1

c₁ /c₂   = 8/k + 3   ≠  - 1

=> -8  ≠ k + 3

=> k ≠  -11

hence k = 3is 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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