Question

Find the value of k for which the system of equations

5x – 3y = 0, 2x + ky = 0

has a non-zero solution.

Answer 1

The given system of equations:

5x – 3y = 0   ...(i)

2x + ky = 0   ...(ii)

These equations are of the following form:

a₁x + b₁y + c₁ = 0, a₂x + b₂y + c₂ = 0

where, a₁ = 5, b₁ = –3, c₁ = 0 and a₂ = 2, b₂ = k, c₂ = 0

For a non-zero solution, we must have:

`(a_1)/(a_2) = (b_1)/(b_2)`

⇒ `5/2 = (-3)/k`

⇒ 5k = –6 

⇒ k = `(-6)/5`

Hence, the required value of k is `(-6)/5`.