-<p>Here is a diagram that consolidates several of our theorems from this section, and which is of practical use when you analyze systems of equations.

+<p>Here is a diagram that consolidates several of our theorems from this section, and which is of practical use when you analyze systems of equations. Note this presumes we have the reduced row-echelon form of the augmented matrix of the system to analyze.

<title>Decision Tree for Solving Linear Systems</title>

column sep=0em, text height=1.5ex, text depth=0.25ex]

<![CDATA[{ & & \text{Theorem RCLS} & \\

& \text{Consistent}& &\text{Inconsistent}\\

-& \text{Theorem ~~FV~~CS}& & \\

+& \text{Theorem CSRN}& & \\

\text{Infinite Solutions}& & \text{Unique Solution}& \\