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Solve using the elimination method and they tell us the sum of two numbers is 70

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Their difference is 24. What are the two numbers? So let's use this first sentence. Let's construct an equation from

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this first sentence. Lets construct an constraint. The sum of two numbers, lets call them x and y.

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So their sum, x + y is equal to 70. That's what this first sentence tells us.

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The second sentence tells us their difference is 24. So that means that x minus y is equal

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to 24. We're going to assume that x is the larger of the two numbers and y is the smaller one.

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So when you take a difference like this you get a positive 24. So you have system of two

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equations with two unknowns and they want us to solve it using the elimination method so let's

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do that. So we can literally just add these two questions. On the left side we would have a positive

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y and a negative y over here, and they would just cancel out. So if we were to just add these equations, they would

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cancel out, so if we were able to just add these two equations we would be able to eliminate

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the y's. So lets do that. So (x plus y) plus (x minus y). Well the plus y and the minus y

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cancel out and you're left with x plus an x which is 2x. And that is going to be equal to 70 plus

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24. 70 plus 24 is equal to 94. And I want to make it clear. I mentioned it in previous videos.

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That this process of adding equations to each other. This is nothing new, we're really just

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adding the same thing to both side of this equation. You could say we're adding 24 to both sides of t

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this equation. Over here we're explicitly adding 24 to the 70. And over here you could say

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we could add 24 to x plus y. But the second constraint tells us that x minus y is the same thing

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as 24. So we're adding the same thing to both sides. Here we're calling it 24, here we're calling it

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x minus y. And we were able to eliminate the y. So we get 2x is equal to 94 now we can divide both sides

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by 2. And we are left with x is equal to 47.

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And now we can substitute back into either one of these equations to solve for y.

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So let's try this first one over here. So we have 47 plus y is equal to

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70. We can subtract 47 from both sides of this equation. So we subtract 47 and we are left with

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y is equal to 23. And you can verify that this works. If you add the two numbers

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47 plus 23 you definitely get 70. If you take 47 minus 23 you definitely get 24.

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So it definitely meets both constraints.