Question

the equation x/k+y/2+6=0 and 8x + y/k + 2=0 have no solution . Find the value of k​

Answer 1

Given:

x/k+y/2+6=0 and 8x + y/k + 2=0 have no solution.

To Find:

the value of k​

Solution:

1) The pair of linear equations represented by these lines a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0

2) If a₁/a₂ = b₁/b₂ ≠ c₁/c₂ then the pair of linear equations has no solution.

3) In this question a₁ = 1/k, b₁= 1/2, c₁ = 6

                             a₂ = 8,   b₂ = 1/k,c₂ = 2

4) As per the rule

we get,

• 1/k/8 = 1/2/1/k

• 1/8k = k/2

• 2 = 8k²

• 1/4 = k²

k = ± 1/2