Study Guide

Systems of Equations

Systems of Equations Introduction

You are sitting at a table with a few pieces of paper and a box of crayons. You draw a line with a red crayon. You draw another line with a blue crayon to make an X. Congratulations! You just graphed a system of equations and found the intersection. You might even notice the little purple dot of the intersection where the red mixed with the blue. You had no idea that you have been solving systems of equations since you were four years old.

In this chapter, you will learn many things: finding the intersection of two lines, finding the intersection of three planes, and even finding the intersection to two regions. This chapter is all about systems of equations and inequalities, and just to spice things up, there are a lot of matrix operations in here as well to make things easier for solving.

To add to the party, we'll show you how to break polynomials into partial fractions. (Doesn't that sound like fun? We're talking Barrel of Monkeys, here.) But after you get through this, we assure you that this precalculus chapter will be a breeze. You might even feel prepared for calculus or a linear algebra class in college.

Systems of Equations Resources

Games and Tools

Crazy 3D Equations
This is a neat 3D function grapher and allows you to see functions in 3D space. This is helpful in visualizing an equation that has an x, y, and z variable.

For All Those Graphing Calculator Fanaticts
Graph lines, inequalities, systems of equations, this calculator can do it all.

Hoop Shoot
Baller! Play some hoops with this Systems of Equations game modeled after a basketball game. This game can take 2 or 4 players.

You Do the Matrix Math
Do you want to double check your matrix calculations? Here's a nice online matrix calculator that has everything including transpose and inverse matrix operations.

Matrix Calculations Aren't Just for TI-84's Anymore
Here's another matrix calculator if you don't have a calculator that can do matrix operations. This one is very user-friendly!

Matrix Row Operation Tool
This coolio toolio can do elementary row operations on a matrix! It was developed at Hofstra University and allows you to type in a matrix, multiply rows by a number and add to different rows. It will even reduce the matrix and swap rows.

Websites

These Guys Know Math
This is the gold standard for calculating things and crunching numbers. Wolfram Alpha can even take an algebraic fraction and decompose it into partial fractions.

Matrix Math Walk-Through
The folks at hotmath explain elementary row operations. This will be helpful if you need some more examples when solving systems of equations with matrices.

Fraction Decomposition
Here's a step by step guide on how to decompose partial fractions – for dummies. Yet another link to help develop your knowledge of this complicated topic.

When Equations Get Non-Linear
Paul has some good notes here about solving systems of non-linear equations. He delves into some advanced problems involving complex roots.