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 )

Graphing systems of equations

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

Simple elimination practice

VIDEO 4:18 minutes
Practice solving systems of equations through simple elimination (exercise at http://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/e/systems_of_equations_with_elimination_0.5 )

Systems of equations with simple elimination

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

Systems of equations with elimination

PRACTICE PROBLEMS
Solving systems of equations with elimination.

Talking bird solves systems with substitution

VIDEO 5:21 minutes
Solving systems of equations with substitution.

Practice using substitution for systems

VIDEO 4:21 minutes
Example doing Khan Academy systems of equations exercise at: http://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/e/systems_of_equations_with_substitution

Systems of equations with substitution

PRACTICE PROBLEMS
Solve systems of equations using substitution

Systems of equations

PRACTICE PROBLEMS
Solve systems of equations with substitution and elimination.

Systems of equations word problems

PRACTICE PROBLEMS
Word problems with systems of equations.

Inconsistent systems of equations

VIDEO 9:25 minutes
Systems of equations without a solution

Infinite solutions to systems

VIDEO 7:08 minutes
Consistent, but dependent systems of equations

Consistent and inconsistent systems

VIDEO 5:29 minutes
Consistent and Inconsistent Systems

Independent and dependent systems

VIDEO 5:10 minutes
Independent and Dependent Systems

Practice thinking about number of solutions to systems

VIDEO 6:36 minutes
Going through a few examples on the Khan Academy practice exercise: http://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/e/solutions_to_systems_of_equations

Systems with one, zero, or infinite solutions

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