In each of the following systems of equations determine whether the system has a unique solution, 2x+3y =7; (k+1) x+(2k-1) y-(4k+1)=0

Question

In each of the following systems of equations determine whether the system has a unique solution, no n solution or infinitely many solutions. In case there is a unique solution, find it:

2x+3y =7

(k+1) x+(2k-1) y-(4k+1)=0

Answer 1

The given system of equation may be written as

The system of equation is of the form

For a unique solution, we must have

Hence, the given system of equations will have infinitely many solutions, if   k =5.