Question

Find the values of k for which the system
2x+ky -1=0
3x-5y -7 =0
will have (i) a unique solution, and (ii) no solution. Is there a value of k for which the system has infinitely many solutions?

Answer 1

The given system of equation may be written as

It is of the form

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

So, the given system of equations will have a unique solution, if k=-10/3

(ii) The given system will have no solution, if

So, the given system of equations will have no solution, if k=-10/3

For the given system to have infinite number of solutions, we must have

Hence, there is no value of k, for which the given system of equations has infinitely many solutions.