# Systems of equations

Contents

A "system of equations" is when we're dealing with more than one equation at the same time. These tutorials show you how to set up and solve systems of equations.

10 exercises available

This video series covers everything you need to know about systems of equations, through stories about trolls, kings, and cupcakes!

Whether in the real world or a cliche fantasy one, systems of equations are key to solving super-important issues like "the make-up of change in a troll's pocket". This tutorial shows you how to solve systems of equations graphically.

We already know that we can represent the set of all x-y pairs that satisfy a linear equation as a line. If there is a point where two of these lines intersect, then the x-y pair corresponding to that point must satisfy both equations.
Common Core Standards: 8.EE.C.8, 8.EE.C.8a

You can solve a system of equations with either substitution or elimination. This tutorial focuses with a ton of examples on elimination. You'll learn best if you pause the videos and try to do the problem before Sal does. Once you get a hang for things, feel free to skip forward to the exercises.
Common Core Standards: 8.EE.C.8, 8.EE.C.8b

This tutorial is focused on solving systems through substitution. It has more examples than you can shake a dog at. As always, pause the video and try to solve before Sal does. Once you get a hang for things, feel free to skip the rest of the videos and try the exercises. The best way to learn, after all, is to do rather than just listen!
Common Core Standards: 8.EE.C.8, 8.EE.C.8b

Learn about the possible number of solutions of systems of linear equations. Spoiler: There can be a single solution, zero solutions, or infinite solutions. These different cases define the distinctions between "consistent" and "inconsistent" systems, and between "dependent" and "independent" systems.

Now that we are able to solve any kind of system we are given, it's time to use that knowledge to solve some word problems.