8th grade is all about tackling the meat of algebra and getting exposure to some of the foundational concepts in geometry. If you get this stuff (and you should because you're incredibly persistent), the rest of your life will be easy. Okay, maybe not your whole life (no way to avoid the miseries of wedding planning), but at least your mathematical life. Seriously, we're not kidding. If you get the equations and functions and systems that we cover here, most of high school will feel intuitive (even relaxing). If you don't, well.. at least you have high school to catch up. :) On top of that, we will sharpen many of the skills that you last saw in 6th and 7th grades. This includes extending our knowledge of exponents to negative exponents and exponent properties and our knowledge of the number system to irrational numbers! (Content was selected for this grade level based on a typical curriculum in the United States.)
Community Questions

# Systems of equations

All content in “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

## 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

## 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

## 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