What is an example of a basic solution which is not feasible?

Question

In a course of Discrete optimization, we made the distinction between Basic feasible solution and basic solution:
A point z is called a basic solution of P if all equality constraints of P are active at z and a total of n linearly independant (equality or inequality) constrains are active. If, in addition, z $\in$ P, then it is called a basic feasible solution (BFS) But have you an example of Basic solution that is not feasible ?

Answer 1

Let $n=2$ and consider the following linear constraints: \begin{align} z_1 &\le 1\\ z_2 &\le 1\\ z_1+z_2 &\le 1 \end{align} What can you say about $z=(1,1)$?