Solving system of linear equations with two variables

Asked Oct 19 '20 at 09:24

Active Oct 19 '20 at 09:27

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Stuck on this problem:

Given $$2^x + 5^y = 2^y +5^x = 7/10$$ Find $(x + y)^{-1}$

I know it's a system of linear equations problem but unsure how to isolate one variable to get the other. Not looking for a solution but just guidance on how to solve it.

edited Oct 19 '20 at 09:27

Matti P.

6,012

asked Oct 19 '20 at 09:24

Sam Grewal

1

By inspection, $x=y=-1$ is a solution. And by inspection, I mean using the fact that $$\frac1a+\frac1b=\frac{a+b}{ab}.$$ Conveniently, $2+5=7$ and $2\times5=10$. – Andrew Chin Oct 19 '20 at 09:27
Thank you Andrew, I wasn't aware of that one! – Sam Grewal Oct 19 '20 at 09:35

Solving system of linear equations with two variables

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