Prove that the following sets of three lines are concurrent: 3x – 5y – 11 = 0, 5x + 3y – 7 = 0 and x + 2y = 0

Question

Philoid · Accepted Answer

Given:
3x − 5y − 11 = 0 …… (i)

5x + 3y − 7 = 0 …… (ii)

x + 2y = 0 …… (iii)

To prove:

Sets of given three lines are concurrent.

Explanation:

Now, consider the following determinant:

= 3 × 14 + 5 × 7 – 11 × 7 = 0

Hence, the given lines are concurrent.