# Systems of linear equations

Contents

Learn how to interpret solutions to systems of linear equations and solve them.

See how you score on these 20 practice questions

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

Learn what "systems of equations" are, what counts as a solution to such a system, and how we can use graphs to solve them.

Learn about the elimination method, which is a way manipulate systems of equations in order to solve them algebraically. This is actually very similar to the way we manipulate single equations in order to solve them!

Learn about the substitution method, which is another way to manipulate systems of equations in order to solve them.

Learn how to rewrite expressions with variables whose values are unknown, by using another information about those variables. For example, given that a+b=0, express a*b in terms of b alone.

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.

Use everything you learned so far in order to solve any kind of system of equations!

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.