Chapter 11

Systems of Linear Equations

A linear equation consists of variable terms whose exponents are always the number 1. When you have two variables, the equation can be represented by a line. With three terms, you can draw a plane to describe the equation. More than three variables is indescribable, because there are only three dimensions. When you have a system of linear equations, you can look for the values of the variables that work for all the equations in the system — the common solutions. Sometimes there’s just one solution, sometimes many, and sometimes there’s no solution at all.

The Problems You’ll Work On

In this chapter on systems of linear equations, you’ll see the following:

Determining the point of intersection of two lines

Finding a single point of intersection of three planes

Writing expressions for multiple solutions of systems

Writing systems in the echelon form or reduced row echelon form

Decomposing fractions using systems of linear equations

What to Watch ...