System of equations

This course is a part of Algebra (all content), a 20-course Topic series from Khan Academy.

This topic covers: - Solutions of linear systems - Graphing linear systems - Solving linear systems algebraically - Analyzing the number of solutions to systems - Linear systems word problems

This course contains 9 segments:

Systems of equations overview

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

Introduction to systems of equations

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

Equivalent systems of equations and the elimination 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!

Solving systems of equations with substitution

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

Manipulating expressions with unknown variables

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.

Number of solutions to systems of equations

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.

Systems of equations word problems

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.

Solving equations by graphing (Algebra 2 level)

Learn how to approximate the solution to any equation by using the power of graphs.

Systems with three variables

Learn how to make the most out of the familiar algebraic techniques in order to solve systems of three equations with three variables.