Find the value of k for which each of the following systems of equations has a unique solution:

4x – 5y = k, 2x – 3y = 12.

Given: 4x – 5y = k – eq 1


2x – 3y = 12 – eq 2


Here,


a1 = 4, b1 = - 5, c1 = - k


a2 = 2, b2 = - 3, c2 = - 12


Given systems of equations has a unique solution




Here, the system of equations have unique solutions, irrespective of the value of k.


That is solution of the given system of equations is independent of the value of k.


k is any real number


8