Question

For what value of k , the pair of linear equation 3x + y = 3 and 6x + ky = 8 does not have a solution .​

Answer 1

Given info : the pair of linear equation 3x + y = 3 and 6x + ky = 8 does not have a solution.

To find : the value of k.

Solution : given equations are ;

3x + y = 3⇒3x + y - 3 = 0 ........(1)

6x + ky = 8⇒6x + ky - 8 = 0 ......(2)

here, a₁ = 3, b₁ = 1 and c = -3

a₂ = 6, b₂ = k and c₂ = -8

Condition : the system doesn't have any solution only if,

a₁/a₂ = b₁/b₂ ≠ c₁/c₂

so, 3/6 = 1/k ≠ -3/-8

⇒1/2 = 1/k ≠ 3/8

⇒k = 1/2 , k ≠ 8/3

Therefore the value of k should be 1/2.