Whenever you're given two equations at the same time, they're called simultaneous equations, so to solve them you'll have to use some fancy math. In this chapter my videos cover the two methods everyone uses, "elimination" and "substitution". Elimination is the one that students prefer by wide margins, yet substitution is the one you're going to keep seeing some version of for the rest of your math career, so it's really best to be familiar with both. In other news, when the two equations in question happen to be the equations of lines (they have x & y in them), the solution is the point of intersection of the lines, which I cover in detail in a video below.
Solving Systems of Simultaneous Equations with Elimination
Elimination is the "canceling" method of solving two equations with two unknowns, in which you add or subtract the two equations to try and cancel one of the variables. In this video I do a few examples, from easy to hard.
Solving Systems of Simultaneous Equations with Substitution
Most kids I tutor dislike this method, preferring elimination. Quite frankly, so do I. But sometimes elimination is too hard because the numbers don't work out, or there are fractions involved, or the teacher's instructions demand substitution. In this video, I try to make it make sense.
Solving 3 Simultaneous Equations with 3 Unknowns
These take a lot longer than the two-equation problems, but they aren't so bad. In this video I show you step-by-step how to get it done quick, and I also show you how to tackle the tricky problem every teacher uses: leaving a variable or two out of some of the equations.
Finding the Intersection of Lines (the graphing method)
While doing your systems homework, you probably noticed that they usually used x and y as the two variables. That wasn't a coincidence. Turns out that the answers you get are the point of intersection of the lines if you had graphed them.
If you do not have an account, you should get one, because it is awesome! You can save a playlist for each test or each chapter, and save your "greatest hits" into a "watch right before the final" list (not that we recommend cramming, but when in Rome...)