For what value of k, the system of equations

Have (i) a unique solution, (ii) no solution? Also, show that there is no value of for which the given system of equation has infinitely namely solutions

Solution:

The given system of equations:

And,
The equations are of the following form:

where, and

(i) For a unique solution, we must have:
that is,
Therefore for all the real values of other than 10, the given system of equations will have a unique solution.

(ii) In order that the given system of equations has no solution, we must have:

As a result, the required value of is 10
There is no value of for which the given system of equations has an infinite number of solutions.