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