I have this problem that I can't solve:

1/x + 1/y = 5/6
1/x - 1/y = 1/6


The book says the answer is (2,3)

Please help.

So you are to show how to solve for x & y?

Quote:

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Originally Posted by adam_89

So you are to show how to solve for x & y?

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Yes

Add the two equations together, which leaves you with an equation in x only. After solving that for x, plug your x-value result back into both original equations and solve for y, making sure that your results for y are consistent.

In other words, use elimination. Note the y term is already a positive and negative of the same value, so you're all set to go. Don't let the fractions throw you off.

(Doing substitution would just be icky.)

So, just adding the equations gives you 2/x = 1

To make it look less icky, you can multiply top and bottom equations by 6 and add, but you can add 1/6 and 5/6 and you can subtract 1/y from 1/y and you can add 1/x and 1/x. The fractions should not intimidate you.