Question

2x-3y=8. 2(k-4)x-ky=k+3​

Answer 1

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