Question

If the equations 5x + ky = 3 and kx + 5y = 3 represent the same line then k = _____.
1. 1
2. 5
3. 3
4. None of these

Answer 1

Correct Answer - Option 2 : 5

Given:

5x + ky = 3

kx + 5y = 3

Concept used:

a₁x + b₁y = c₁

a₂x + b₂y = c₂

(a₁/a₂) = (b₁/b₂) = (c₁/c₂)

Calculation:

a₁ = 5, b₁ = k, c₁ = 3

a₂ = k, b₂ = 5, c₂ = 3

⇒ a₁/a₂ = b₁/b₂ = c₁/c₂

⇒ 5/k = k/5

⇒ k² = 25 = k = √25

⇒ k = 5

⇒ c₁/c₂ = 3/3 = 1

Now,

(a1/a2) = (b1/b2) = (c1/c2) = 1

∴ The value of k is 5

 Here k will not be ± 5

If we take k = ± 5, then it will be

a1/a2 = b1/b2 = -1 

But, c1/c2 = 3/3 = 1

Which does not satisfy the required condition.

So, k ≠ ± 5