Alright, folks. So let's get some more practice here figuring out what to multiply our equations by. I've got these two equations over here, 5x+3y=10. And then I've got −7x+5y=15. Let's go through our different possibilities and figure out what to multiply these equations by. Alright? So are they equal with opposite signs? Are any of the coefficients, either the x or y, equal with opposite signs? Let's see. I got 5 and negative 7 and then 35, so definitely not. They're also not equal with the same sign either. I've got all these different coefficients. Do I have any coefficients that are factors of each other? So, for example, are 5 and negative seven factors of each other? No. Are 35 factors of each other? Also, no. We've got no situation here where they’re factors of each other, so we just have to multiply the smaller equation or the smaller coefficients by the quotient. So if it's none of these, then remember, kind of by default, we can just look at this one. If it's anything else, then one situation that will always work no matter what is we can multiply each equation by the other coefficients. So here's what I mean by this. I've got 5 and negative 7. Notice how these two things are already opposite signs. So what I can do is I can multiply this top equation by 7, and then I can multiply this bottom equation by 5. Because notice how what’s going to happen is that 7 times 5 will give you a number, and 5 times 7 will give you the same number, but the negative sign will make them opposites. So all I have to do is kind of just multiply them by each other's coefficients, and this is what happens here. So when I multiply this top equation by 7, I'm going to multiply all the coefficients and 7×5=35x,7×3=21y,7×10=70. And on the bottom here, what you'll get is when you do 5×−7=−35x,5×5=25y,5&#... ×15=75. See how now we've gotten the same numbers, but opposite signs? Now when you go ahead and you add these two equations together, remember, this will always work no matter what situation you have. Obviously, the math gets a little sort of tedious, and you might get some big numbers. But notice how the x coefficients will cancel as promised, and then all we have to do is just add the rest. So 21y+25y=46y,70+75=145. Now again, the math is going to be kind of ugly here, but you'll actually notice here that you can solve for this variable. So you just divide by 46 from both sides, and what you would get is you would end up getting that y is equal to 145÷46. Now that's not a clean number, but it actually doesn't matter because it is still going to be the solution to your y variable. Alright? So now you can take this y variable, and you can plug it into the other equations and solve for the x variable. Alright? But this is what you would multiply these equations by in order to get one of your coefficients to cancel. Thanks for watching, and I'll see you in the next one.