You probably noticed that the process we used to solve linear systems in Section 2.2 is almost identical to the process we used to solve linear systems in Section 2.4.

To make this concrete, let’s compare the steps for the system

In the table below, the steps for solving the system using elimination are shown on the left side in blue. The steps for matrix elimination are shown on the right in green. You can click on the table to make it larger.

Notice that each step for elimination corresponds to an almost identical step in matrix elimination. The main difference is the absence of the variable in matrix elimination.