Question

find the value of k : x + 5y = 9 and 3x + ky = 8

Answer 1

Given : x + 5y = 9 and 3x + ky = 8

has unique solution

To Find : value of k

Solution:

A pair of linear Equations

a₁x + b₁y  = c₁  &

a₂x + b₂y = c₂

has unique Solution  if

a₁/a₂  ≠ b₁/ b₂

  x + 5y = 9

 3x + ky = 8

1/ 3  ≠  5/k

=> k ≠  15

k ≠  15  , has unique solution

a₁/a₂  = b₁/ b₂ = c₁/ c₂ = Infinite solution

( not possible is this case)

a₁/a₂  = b₁/ b₂ ≠ c₁/ c₂ = no  solution

k = 15 no solution

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