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An electronics warehouse ships televisions and DVD players in

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certain combinations to retailers

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throughout the country.

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They tell us that the weight of 3 televisions and 5 DVD

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players is 62.5 pounds, and the weight of 3 televisions

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and 2 DVD players-- so they're giving us different

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combinations-- is 52 pounds.

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Create a system of equations that

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represents this situation.

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Then solve it to find out how much each television and DVD

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player weighs.

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Well, the two pieces of information they gave us in

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each of these statements can be converted into an equation.

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The first one is is that the weight of 3 televisions and 5

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DVD players is 62.5 pounds.

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Then they told us that the weight of 3 televisions and 2

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DVD players is 52 pounds.

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So we can translate these directly into equations.

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If we let t to be the weight of a television, and d to be

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the weight of a DVD player, this first statement up here

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says that 3 times the weight of a television, or 3

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televisions, plus 5 times the weight of a DVD player, is

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going to be equal to 62.5 pounds.

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That's exactly what this first statement is telling us.

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The second statement, the weight of 3 televisions and 2

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DVD players, so if I have 3 televisions and 2 DVD players,

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so the weight of 3 televisions plus the weight of 2 DVD

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players, they're telling us that that is 52 pounds.

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And so now we've set up the system of equations.

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We've done the first part, to create a system that

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represents the situation.

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Now we need to solve it.

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Now, one thing that's especially tempting when you

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have two systems, and both of them have something where, you

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know, you have a 3t here and you have a 3t here, what we

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can do is we can multiply one of the systems by some factor,

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so that if we were to add this equation to that equation, we

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would get one of the terms to cancel out.

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And that's what we're going to do right here.

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And you can do this, you can do this business of adding

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equations to each other, because remember, when we

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learned this at the beginning of algebra, anything you do to

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one side of an equation, if I add 5 to one side of an

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equation, I have to add 5 to another side of the equation.

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So if I add this business to this side of the equation, if

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I add this blue stuff to the left side of the equation, I

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can add this 52 to the right-hand side, because this

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is saying that 52 is the same thing as this thing over here.

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This thing is also 52.

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So if we're adding this to the left-hand side, we're actually

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adding 52 to it.

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We're just writing it a different way.

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Now, before we do that, what I want to do is multiply the

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second, blue equation by negative 1.

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And I want to multiply it by negative 1.

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So negative 3t plus-- I could write negative 2d is equal to

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negative 52.

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So I haven't changed the information in this equation.

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I just multiplied everything by negative 1.

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The reason why I did that is because now if I add these two

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equations, these 3t terms are going to cancel out.

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So let's do that.

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Let's add these two equations.

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And remember, all we're doing is we're adding the same thing

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to both sides of this top equation.

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We're adding essentially negative 52 now, now that

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we've multiplied everything by a negative 1.

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This negative 3t plus negative 2d is the same thing as

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negative 52.

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So let's add this left-hand side over here.

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The 3t and the negative 3t will cancel out.

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That was the whole point.

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5d plus negative 2d is 3d.

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So you have a 3d is equal to 62.5 plus negative 52, or 62.5

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minus 52 is 10.5.

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And now we can divide both sides of this equation by 3.

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And you get d is equal to 10.5 divided by 3.

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So let's figure out what that is.

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3 goes into 10.5-- it goes into 10 three times.

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3 times 3 is 9.

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Subtract.

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Get 1.

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Bring down the 5.

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Of course, you have your decimal point right here.

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3 goes into 15 five times.

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5 times 3 is 15.

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You've got to subtract, and you get a 0.

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So it goes exactly 3.5 times.

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So the weight of a DVD player-- that's what d

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represents-- is 3.5 pounds.

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Now we can substitute back into one of these equations up

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here to figure out the weight of a television.

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We can just use that top equation.

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So you get 3t plus 5 times the weight of a DVD player, which

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we just figured out is 3.5.

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Remember, we're just looking for values that satisfy both

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of these equations.

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So 5 times 3.5-- needs to be equal to 62.5.

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So you get 3t plus-- what is this going to be?

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This is going to be 15 plus 2.5, right?

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5 times 0.5 is 2.5, 5 times 3 is 15.

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So it's 17.5, is equal to 62.5.

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Now we can subtract 17.5 from both sides of this equation.

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And what do we get?

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The left-hand side is just going to be 3t.

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This cancels out, that was the whole point of it.

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3t is going to be equal to-- let's see.

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The 0.5 minus 0.5, that cancels out.

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So this is the same thing as 62 minus 17.

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62 minus 7 would be 55.

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And so we're going to subtract another 10.

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So it's going to be 45.

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So this is going to be equal to 45.

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Now you can divide both sides of this equation by 3.

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And we get t is equal to 15.

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So we've solved our system.

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The weight of a DVD player is 3.5 pounds, and the weight of

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a television is 15 pounds.

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And we're done.

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