Question

For what value of λ are the three lines 2x – 5y + 3 = 0, 5x – 9y + λ = 0 and x – 2y + 1 = 0 concurrent?

Answer 1

Given:
2x − 5y + 3 = 0 … (1)

5x − 9y + λ = 0 … (2)

x − 2y + 1 = 0 … (3)

It is given that the three lines are concurrent.

Now, consider the following determinant:

2(-9 + 2λ) + 5(5 – λ) + 3(-10 + 9) = 0

-18 + 4λ + 25 – 5λ – 3 = 0

λ = 4

∴ The value of λ is 4.