Prove that the following sets of three lines are concurrent:

and y = x.

Given:
bx + ay – ab = 0 … (1)

ax + by – ab = 0 … (2)

x − y = 0 … (3)

To prove:

Sets of given three lines are concurrent.

Explanation:

Now, consider the following determinant:

-b × ab - a × ab – ab × (-a – b) = 0

Hence proved, the given lines are concurrent.