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# help algebra

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2/x + 2/y = 30

x + y = 10

If the above equations are true simultaneously, then find the value of xy.

Jul 7, 2021

#1
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We can start off my multiplying the first equation by $xy$,

$$2y+2x=30xy \\ x + y = 15xy$$

Our second equation has the same exact left side, so our right sides are equivalent too.

$$10 = 15xy \\ \frac{10}{15} = xy \\ \frac{2}{3} = xy$$

So $xy = \frac{2}{3}$

Jul 7, 2021