Question

The value of 'k' for which the pair of linear equations x + y − 4 = 0 and 2x + ky − 8 = 0 has infinitely many solutions is ______.

विकल्प

• k ≠ 2

• k ≠ −2

• k = 2

• k = −2

Answer 1

The value of 'k' for which the pair of linear equations x + y − 4 = 0 and 2x + ky − 8 = 0 has infinitely many solutions is k = 2.

Explanation:

Given, x + y − 4 = 0

2x + ky − 8 = 0

Here, a₁ = 1; b₁ = 1; c₁ = − 4

And, a₂ = 2; b₂ = k; c₂ = − 8

For infinitely many solutions: `"a"_1/"a"_2 = "b"_1/"b"_2 = "c"_1/"c"_2`

Substituting, the value we get is: `1/2 = 1/"k" = (-4)/(-8)`

Thus, `1/2 = 1/"k"` ⇒ k = 2

or `1/"k" = (-4)/(-8)` ⇒ k = 2

Thus, the value of k = 2 for infinitely many solutions.