So a lot of times in physics, you're going to end up having an equation in which you don't have enough information to solve it, so you're going to get another equation, and now you have to deal with these two equations over here. This is called a system of equations, and we're just going to review how to solve these really quickly. Basically, what we're going to do is we're going to substitute one equation into the other to reduce the number of variables. I'm going to show you how this works. The first thing we're going to do here is if you have two equations, you're going to solve one equation for, let's say, the y variable or whatever the easiest one is to solve. In this case, I've got y equals 3x minus 6, so I've got already y by itself.
Now what we're going to do here is we're going to plug the right side of this equation a in for whenever we see y in equation b. So, basically, what I'm going to do here is I'm going to take 3x minus 6, and everywhere I see y in equation b, I'm going to replace it with 3x minus 6. So what this looks like over here is it looks like 2x plus 3x minus 6. This ends up just being 3x minus 6. It's not y anymore. I'm just going to replace it with 3x minus 6, and this equals 4. Notice that what I've done with this equation is now instead of having two variables, I only have one. And now I can just go ahead and solve for x, and that's what my third step is. You just solve this for x, and we know exactly how to do this. So this 2x plus 3x just becomes 5x minus 6 is 4, and then all I have to do is just move the 6 over to the other side, and basically, I end up with 5x equals 10. So now all I have to do is divide each side by 5, and what I end up with is x equals 2, and that's the answer.
This is the answer; that's my x value that works for both of these equations, but I'm not quite done yet because this is only one of the values that works for both of the equations. I need to also figure out what the y value is, since that's the fourth step. You're going to take this x value that you've already figured out, and you can actually plug it into either one of these two equations to solve for y. So you could plug it into a or b. It actually doesn't matter. So let's go ahead and do this. This is going to be y equals 3, and now we don't have just x because we know what x is. X is just equal to 2, so we plug this back in. So 3 times 2 minus 6. This ends up just giving us 6 minus 6 over here, and so this gives us a y value of 0. Alright? So in other words, the solution to both of these equations is actually when x is 2 and y is equal to 0. So this represents the xy solution that satisfies both of the equations. Alright? And that's the y value. So that's how to solve a system of equations by substitution.