Study Guide

Systems of Equations and Inequalities Introduction

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Systems of Equations and Inequalities Introduction

Like any superhero of worth, Shmoop has acquired a nemesis or two over the years. Now our old adversaries are starting to team up to try and take us down. We've tangled with systems of equations before, and we've also deftly dealt with inequalities, but can we take both on at once? The answer is, "Of course." Shmoop doesn't back down from a math challenge.

Even if we succeed, though, an even greater threat is coming: systems of equations with three variables. It's a good thing we're going to practice graphing and solving two-variable equations first. We've gotta learn to juggle with two flaming torches before we can throw in that third one.

Whether we're dealing with an equality or an inequality, two or three variables, we'll swoop in and save the day, giving you quality advice for getting the right answer, easy-peasy.

Systems of Equations and Inequalities Resources


Cool Math—3x3 Systems of Equations
Math so cool, it's ice cold. Covers systems with three equations, including all the freaky stuff that happens when there isn't one solution. The site also includes games and the much-, much-needed stress relief section.

Solving Systems of Inequalities—Free Math Help
This website goes all the way back to the very basics about inequalities. If you just need a break, play the Alien Attack game.

Paul's Online Math Notes—Linear Systems with Three Variables
Paul knows his stuff, and he'll make sure you know his stuff, too.


All I Do Is Solve (WSHS Math Rap Song)
What rhymes, what rhythm. Get up and shake down with this math rap about solving systems of equations.

Patrick JMT—Solving Systems of Equations Using Elimination By Addition
Patrick's soothing voice guides us through the elimination method, with a number of thoroughly explained problems.

Not only does this place have a ton of videos, they also have multiple videos by different people explaining the same problem, each in their own way. Some of their explanations are in Spanish, too. Shmoop approves.

Khan Academy: Algebra
Take another crack at that 3D graph with a well-done video by Khan.

Games and Tools

Algebra vs The Cockroaches
Test your knowledge and skill as you race against the cockroaches to find the equation of a line in slope-intercept form. Smashing them with a rocket is surprisingly therapeutic.

3 x 3 Equation Solver
Don't own a graphing calculator? Never fear—here's a free calculator to quickly solve systems of equations. Simply plug in your coefficients and constants and *bam* instant answers. We trust you to use it to only check your answers.

Calling all crossword lovers…if you happen to want math vocabulary in your crossword puzzles. They also have flip cards and pinball.

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