# Systems of linear equations

Contents

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

Try some practice problems

Learn by doing or check your understanding

Learn what "systems of equations" are and what counts as a solution to such a system.

Learn how to solve a system of equations by considering its graph, which turns out to be a VERY effective method.

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 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.

Learn how to determine the number of solutions a system of equations has, without having to go through the entire solution process.

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.