Algebra

Hello gents. Trying to help my girlfriend's daughter with some math & I didn't realize how bad I am with algebra. I'm not looking for an answer. Just an explanation on how this is solved. Any help is appreciated.

The question is:

Quote:

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Solve for the indicated variable

4/xy + 16/xz + 20/yz = 12

Solve for y.

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I'm thinking divide by Y. I've been out of high school too long.

Multiply through by xyz and then collect terms....

What you want eventually is to get an expression that looks like

Code:

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y = ...

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(This is what solving for y means)

How do you do that? Well, in this case, y appears in a fraction as the denominator a few times. You don't want that, so how do you get rid of that? The answer is: multiply by y! Since

Code:

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(1/y) * y = y/y = 1

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you got rid of the y.

If there is some other stuff in the equation it works the same way:

Code:

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(abc/y) * y = abc * (y/y) = abc

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or

Code:

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(abc/xy) * y = abc * (y/xy) = (abc/x) * (y/y) = abc/x

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Visualize this too instead of just thinking of it as multiplication. If an y appears in the denominator, you multiply by y (to make "1") to get rid of it.

Of course, to keep the equation valid you'll have to multiply all other terms by y too. In this case that means:

Code:

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4/xy + 16/xz + 20/yz = 12
4/x + 16y/xz + 20/z = 12y

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Now the final step is to collect the terms that have y in them on one side, and put the remaining terms on the other side.