How do you know when to use an augmented matrix?

Question

Bit confused please can someone clarify. 

Answer 1

To solve a system of n linear equations with n unknowns (variables), that's exactly when you employ an augmented matrix (n rows, n+1 columns), with the last column consisting of all the constant-only values from the n equations.

 

You can use the RREF matrix method (on TI-83 or -84 calculators, and several other makes/models) to solve easily & reliably.