Find the value of k for which the system of linear equations has an infinite number of solutions:

Solution:

Given system of equations:

And,

Equations are of the following form:

where, and
For an infinite no. of solutions, we must have:

We have the following three cases:

Case I:

Case II:







or

Case III:

As a result, the given system of equations has an infinite no. of solutions when is equal to 4.