The variable chosen by Rule 1 is called the entering variable. Here let us choose, say, x1 as our
entering variable. It really does not matter which variable we choose as long as it has a negative
coecient in Row 0. The idea is to pivot in order to make the nonbasic variable x1 become a basic
variable. In the process, some basic variable will become nonbasic (the leaving variable). This
change of basis is done using the Gauss-Jordan procedure. What is needed next is to choose the
pivot element. It will be found using Rule 2 of the simplex method. In order to better understand
the rationale behing this second rule, let us try both possible pivots and see why only one is
acceptable.