Question

Find the value of k for which the system of equations 2x + 3y – 5 = 0 and 4x + ky – 10 = 0 has infinite number of solutions.

Find k for which the system 2x + 3y – 5 = 0, 4x + ky – 10 = 0 has an infinite number of solutions.

Answer 1

The given system is

2x + 3y – 5 = 0   ...(i)

4x + ky – 10 = 0   ...(ii)

Here, a₁ = 2, b₁ = 3, c₁ = –5, a₂ = 4, b₂ = k and c₂ = –10

For the system, to have an infinite number of solutions, we must have

`(a_1)/(a_2) = (b_1)/(b_2) = (c_1)/(c_2)`

⇒ `2/4 = 3/k = (-5)/(-10)`

⇒ `1/2 = 3/k= 1/2`

⇒ k = 6

Hence, k = 6.