Everyone, let's get started here. So we're going to get some more practice with what to multiply your equation or equations by in order to eliminate one of your variables. The whole idea is that you could take these two equations here. We're going to have to multiply one or both of them by some number because we want either the x or the y coefficients to cancel out when we add them. Alright? So I just want to mention here that we're actually not going to fully solve the problem, and I also want to mention that there isn't actually one correct way to do this. There are actually many different correct answers. So without further ado, let's go ahead and get started and break it down here. We've got these two equations: x2 + y3 = 1 and x - y = 3. Now remember here, we're just going to have to figure out what to multiply these variables by to get them to cancel. So if you look at this, we could look at the x coefficients. Right? I've got x2 and I've got x1. So notice how this is kind of like an implied one over here. Let's just go through the different sort of possibilities. Are they equal with opposite signs? No. They're not, so we're not just going to do this. Are they equal with the same sign? They're not either, so we're not going to do any of this. But they are factors of each other. So in other words, you know, 2 is a factor or, sorry, 1 is always a factor of anything else. So what you could do is you can multiply this equation with the smaller coefficients by the quotient. What does that mean? It means the equation with the smaller coefficients over here, we're going to have to multiply by the difference or, sorry, the quotient between these coefficients, 2/1, which means we're going to multiply it just by 2. Now, one of the things you might notice here is if you multiply by 2, what you're going to get is x2 at the bottom, and notice how both of those are going to have the same sign. So whenever you're doing this, you could always just multiply by a negative number so that you get the signs to be opposite. So we're not going to multiply by 2, we're going to multiply by negative 2. So let's go ahead and do that. If I bring the system of equations down, I'm going to rewrite this x2 + y3 = 1. And then what happens is the negative two times one becomes negative two x. The negative two into the negative y is going to become a positive two y, and it has to flip sign. And the negative two going into the three is going to be negative six. So everything gets multiplied by two and then flips the sign. Alright? So now that we've done this, notice how when you sort of set these equations up and compare their coefficients, when you add these things together, the x's now will cancel. And then the y3 plus the y2 will actually become y5. And then your one and negative six will actually just become negative five. Alright? So again, what you're going to do here is, you know, we don't have to fully solve this problem, but what you'll see here is that you'll see that y = -1. Now once you get this, remember, you can always just plug these back into the other equations to figure out x, but we're not going to do that because we don't want to actually fully solve the problem. So this is definitely one of the things that you could have done. You could have multiplied by negative 2. But I'm actually going to show you that there is another possibility. You could have looked at this problem a little bit differently. So I'm going to go ahead and rewrite this here and show you another sort of very common possibility that you could have seen. So x2 + y3 = 1, and then I've got x - y = 3. Now, you could have looked at these two equations here and could have looked at the fact that the y coefficients already have an opposite sign. And so you could have chosen to focus on those and that would have been perfectly fine here. So, again, let's go through the possibilities. Are they equal with opposite signs? They're not. Are they equal with the same signs? They're not, but they a