WEBVTT
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We already set up for you.
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We have a third scenario where you need to find a least common multiple.
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Because if you look at our coefficients of x, we have two and five.
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Well, those aren't going to drop out if we had our subtract.
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You look at our y-coefficient, we have three and four.
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Those aren't going to drop out if we had our subtract.
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So we need to find a least common multiple.
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In other words, we need to find the smallest number
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that both coefficients divide into.
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And it's just up to you.
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You can decide which term you want to get rid of, either the x term or the y term.
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In this instance, I'm going to choose to get rid of the x term.
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So I need to think to myself, what's the smallest number
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that both two and five divide evenly into?
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That would be 10.
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10 is the least common multiple.
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So how do I get two x to become 10x?
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We're going to multiply by five.
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How do I get five x to become 10x?
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We're going to multiply by two.
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And again, you must multiply these factors to everything,
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not just the first term to all the terms.
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Here we go.
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Five times two x gives us 10x.
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Five times three y gives us 15y.
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And five times five is 25.
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Here we have two times five x is 10x.
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Two times four y is eight y.
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And two times 16 is 32.
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We did our distribution.
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We did our multiplication.
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Now we're all set.
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Now, we have the x terms both sharing the same coefficient of 10.
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But just like the previous problem, if we add, we get 20x.
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So that's not going to work.
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Instead of adding, we must make this subtraction.
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And you don't subtract just the 10x.
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You subtract the entire problem.
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So here we go.
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10x, take away 10x, zero.
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That cancels.
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15y, take away eight y, leaves us with 7y.
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And finally, 25, take away 32, brings us to negative 7.
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So now we have 7y equals negative 7.
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Dividing both sides by 7, you get y equals negative 1.
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That's your solution for y.
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Now we just need to get the x.
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Well, what do you do?
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You just take your y equals negative 1.
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Y becomes negative 1.
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And you either replace negative 1 into this y.
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Or you replace negative 1 into that y.
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And you solve.
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And you'll get a solution for x.
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There you have it.
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Nothing too tough.
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Just you have to have a plan.
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And just go through the motions.
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Hope you enjoyed.
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Good luck.
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Thank you very much.