Systems of equations
System for solving the King's problems
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!
If you want more examples, feel free to look at the other tutorials in this topic.
Common Core Standards: 8.EE.C.8, 8.EE.C.8a, 8.EE.C.8b, 8.EE.C.8c
- 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 with elimination practice
- Talking bird solves systems with substitution
- Practice using substitution for systems
- Systems of equations
- Systems of equations word problems
Solving linear systems graphically
We already know that we can represent the set of all x-y pairs that satisfy a linear equation as a line. If there is a point where two of these lines intersect, then the x-y pair corresponding to that point must satisfy both equations.
Common Core Standards: 8.EE.C.8, 8.EE.C.8a
Solving systems with substitution
This tutorial is focused on solving systems through substitution. It has more examples than you can shake a dog at. As always, pause the video and try to solve before Sal does. Once you get a hang for things, feel free to skip the rest of the videos and try the exercises. The best way to learn, after all, is to do rather than just listen!
Common Core Standards: 8.EE.C.8, 8.EE.C.8b
Solving systems with elimination
You can solve a system of equations with either substitution or elimination. This tutorial focuses with a ton of examples on elimination. You'll learn best if you pause the videos and try to do the problem before Sal does. Once you get a hang for things, feel free to skip forward to the exercises.
Common Core Standards: 8.EE.C.8, 8.EE.C.8b
- 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 with elimination practice
Thinking about solutions to systems
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.
Common Core Standards: 8.EE.C.8, 8.EE.C.8b
- Inconsistent systems of equations
- Infinite solutions to systems
- Consistent and inconsistent systems
- Independent and dependent systems
- Practice thinking about number of solutions to systems
- Graphical solutions to systems
- Solutions to systems of equations
- Constructing solutions to systems of equations
- Constructing consistent and inconsistent systems
Systems word problems
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!
Common Core Standards: 8.EE.C.8, 8.EE.C.8b, 8.EE.C.8c
- Using a system of equations to find the price of apples and oranges
- Linear systems word problem with substitution
- Systems of equations word problems
- Systems of equation to realize you are getting ripped off
- Thinking about multiple solutions to a system of equations
- Understanding systems of equations word problems