# Solving systems of equations

14 videos

8 skills

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" or "how can order the right amount of potato chips for a King's party." Join us as we cover (and practice with examples and exercises) all of the major ways of solving a system: graphically, elimination, and substitution. This tutorial will also help you think about when system might have no solution or an infinite number of solutions. Very, very exciting stuff!

### Trolls, tolls, and systems of equations

VIDEO
6:51 minutes

A troll forces us to use algebra to figure out the make-up of his currency. We end up setting up a system of equations

### Solving the troll riddle visually

VIDEO
5:41 minutes

Solving the system of equations visually. Now we can save the prince/princess

### Solving systems of equations graphically

VIDEO
2:22 minutes

Some practice solving systems graphically (exercises available at http://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/e/graphing_systems_of_equations )

### Solving systems of equations graphically

PRACTICE PROBLEMS

Graph a system of equations in slope-intercept or standard form

### King's cupcakes: Solving systems by elimination

VIDEO
9:00 minutes

Using simple elimination to figure out how many cupcakes are eaten by children and adults

### Solving systems of linear equations with elimination example 1

VIDEO
4:18 minutes

Practice solving systems of equations through simple elimination

### Solving systems of linear equations with elimination 1

PRACTICE PROBLEMS

Solve systems of equation with one-step elimination (e.g., x-values or y-values cancel each other out).

### How many bags of potato chips do people eat?

VIDEO
9:21 minutes

Using elimination to solve a system of equations

### Systems with elimination practice

VIDEO
5:31 minutes

Example of solving systems of equations with elimination

### Solving systems of linear equations with elimination 2

PRACTICE PROBLEMS

Solving systems of equations with elimination.

### Talking bird solves systems with substitution

VIDEO
5:21 minutes

Solving systems of equations with substitution.

### Solving systems of linear equations with substitution example

VIDEO
4:21 minutes

### Solving systems of linear equations with substitution

PRACTICE PROBLEMS

Solve systems of equations using substitution

### Solving systems of two linear equations

PRACTICE PROBLEMS

Solve systems of equations with substitution and elimination.

### Analyzing solutions to linear systems graphically 2

VIDEO
6:36 minutes

### Analyzing solutions to linear systems graphically

PRACTICE PROBLEMS

### Systems with one, zero, or infinite solutions

PRACTICE PROBLEMS

Determine how many solutions exist to a given system of equations (one, zero, infinite).