Question

Find the value of k for which the system
kx+2y =5
3x+y = 1
has (i) a unique solution, and (ii) no solution.

Answer 1

The given system of equation may be written as

(i) The given system will have a unique solution, if

So, the given system of equations will have a unique solution, if k ≠  6
(ii) The given system will have no solution, if

So, the given system of equations will have no solution, if

Hence, the given system of equations will have no solution, if k=6.