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.


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