Khan Academy on a Stick
Systems of equations and inequalities
What happens when we have many variables but also many constraints.
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Trolls, Tolls, and Systems of Equations
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
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Solving the Troll Riddle Visually
Solving the system of equations visually. Now we can save the prince/princess
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King's Cupcakes: Solving Systems by Elimination
Using simple elimination to figure out how many cupcakes are eaten by children and adults
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How many bags of potato chips do people eat?
ccUsing elimination to solve a system of equations
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Systems with Elimination Practice
Example of solving systems of equations with elimination
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Talking bird solves systems with substitution
Solving systems of equations with substitution.
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Inconsistent systems of equations
ccSystems of equations without a solution
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Infinite solutions to systems
Consistent, but dependent systems of equations
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Consistent and Inconsistent Systems
Consistent and Inconsistent Systems
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Independent and Dependent Systems
ccIndependent and Dependent Systems
Solving systems of equations for the king
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!
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Visualizing the solution set for a system of inequalities
Visualizing the solution set for a system of inequalities
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Graphing systems of inequalities
ccGraphing systems of inequalities
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Graphing systems of inequalities 2
ccGraphing systems of inequalities 2
Systems of inequalities
You feel comfortable with systems of equations, but you begin to realize that the world is not always fair. Not everything is equal! In this short tutorial, we will explore systems of inequalities. We'll graph them. We'll think about whether a point satisfies them. We'll even give you as much practice as you need. All for 3 easy installments of... just kidding, it's free (although the knowledge obtained in priceless). A good deal if we say so ourselves!
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Systems of Three Variables
ccSystems of Three Variables
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Systems of Three Variables 2
ccSystems of Three Variables 2
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Solutions to Three Variable System
ccSolutions to Three Variable System
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Solutions to Three Variable System 2
ccu14 l3 t1 we4 Solutions to Three Variable System
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Three Equation Application Problem
ccThree Equation Application Problem
Systems with three variables
Two equations with two unknowns not challenging enough for you? How about three equations with three unknowns? Visualizing lines in 2-D too easy? Well, now you're going to visualize intersecting planes in 3-D, baby. (Okay, we admit that it is weird for a website to call you "baby.")
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Non-Linear Systems of Equations 1
ccNon-Linear Systems of Equations 1
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Non-Linear Systems of Equations 2
ccNon-Linear Systems of Equations 2
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Non-Linear Systems of Equations 3
ccNon-Linear Systems of Equations 3
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Systems of nonlinear equations 2
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Systems of nonlinear equations 3
Non-linear systems of equations
Tired of linear systems? Well, we might just bring a little nonlinearity into your life, honey. (You might want to brush up on your solving quadratics before tackling the non-linear systems.) As always, try to pause the videos and do them before Sal does!