Thus, the solution space is presented by m linear equations and n variables. If the numbers of the linear equations and the variables are equal, the system has only one solution. However, the majority of linear programs have a greater number of variables compared equations n>m.

A basic solution whether it is feasible or not is a corner point of the solution space. The corner points of system of equations are obtained by setting n – m number of variables equal to zero and solving the equations for the remaining m number of variables. The number of basic solutions can be calculated as below:

Here, the system has two equations (m = 3) and four variables. (n = 6) Thus, there are 20 basic solutions: