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The following is listed under the "multiple variable" category of my Algebra I homework.

Find all ordered pairs $(x,y)$ that satisfy both $\frac{3x-4y}{xy} = -8$ and $\frac{2x+7y}{xy} = 43$

I can't wrap my head around what to do. Thanks in advance for your help.

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  • $\begingroup$ Note this is a pair of linear equations in $1/x,1/y$. $\endgroup$ Jun 8, 2019 at 11:48

1 Answer 1

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$$\frac{3x-4y}{xy} = \frac{3}{y} - \frac{4}{x} = -8$$

$$\frac{2x+7y}{xy} = \frac{2}{y}+\frac{7}{x} = 43$$

Let $u = \frac{1}{x}$ and $v = \frac{1}{y}$.

Then,

$3v - 4u = -8$ and $2v + 7u = 43$

Solve these linear equations and replace $x$ and $y$.

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