Algebra
Practice this topic
Systems of equations and inequalities
Solving a system of equations or inequalities in two variables by elimination, substitution, and graphing.
Tutorials
A system for solving the King's problems
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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
- Solving the Troll Riddle Visually
- Solving Systems Graphically
- Graphing systems of equations
- King's Cupcakes: Solving Systems by Elimination
- How many bags of potato chips do people eat?
- Simple Elimination Practice
- Systems of equations with simple elimination
- Systems with Elimination Practice
- Systems of equations with elimination
- Talking bird solves systems with substitution
- Practice using substitution for systems
- Systems of equations with substitution
- Systems of equations
- Systems of equations word problems
Super fast systems of equations
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Have no time for trolls, kings and parrots and just want to get to the essence of system. This might be a good tutorial for you. As you can see, this stuff is so important that we're covering it in several tutorials!
- Solving Linear Systems by Graphing
- Graphing systems of equations
- Solving Linear Systems by Substitution
- Systems of equations with substitution
- Solving Systems of Equations by Elimination
- Systems of equations with simple elimination
- Solving Systems of Equations by Multiplication
- Systems of equations with elimination
- Systems of equations
- Special Types of Linear Systems
- Solutions to systems of equations
- Old video on systems of equations
Solving systems graphically
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This tutorial focuses on solving systems graphically. This is covered in several other tutorials, but this one gives you more examples than you can shake a chicken at. Pause the videos and try to do them before Sal does.
Thinking about solutions to systems
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You know how to solve systems of equations (for the most part). This tutorial will take things a bit deeper by exploring cases when you might have no solutions or an infinite number of them.
Solving systems with substitution
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This tutorial is focused on solving systems through substitution. This is covered in several other tutorials, but this one focuses on substitution with more examples than you can shake a dog at. As always, pause the video and try to solve before Sal does.
Solving systems with elimination (addition-elimination)
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You can solve a system of equations with either substitution or elimination. This tutorial focuses with a ton of examples on elimination. It is covered in other tutorials, but we give you far more examples here. You'll learn best if you pause the videos and try to do the problem before Sal does.
- Example 1: Solving systems by elimination
- Example 2: Solving systems by elimination
- Addition Elimination Method 1
- Addition Elimination Method 2
- Addition Elimination Method 3
- Addition Elimination Method 4
- Example 3: Solving systems by elimination
- Simple Elimination Practice
- Systems of equations with simple elimination
- Systems with Elimination Practice
- Systems of equations with elimination
Systems of equations word problems
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This tutorial doesn't involve talking parrots and greedy trolls, but it takes many of the ideas you might have learned in that tutorial and applies them to word problems. These include rate problems, mixture problems, and others. If you can pause and solve the example videos before Sal does, we'd say that you have a pretty good grasp of systems. Enjoy!
- Example 4: Solving a word problem with substitution
- Mixture problems 1
- Mixture problems 2
- Mixture problems 3
- Systems and rate problems
- Systems and rate problems 2
- Systems and rate problems 3
- Officer on Horseback
- Two Passing Bicycles Word Problem
- Passed Bike Word Problem
- Passing Trains
- Overtaking Word Problem
- Problem Solving Word Problems 2
- Systems of equations word problems
Systems of inequalities
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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!
Fancier systems of equations
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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.") 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!