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# Solving equations for the parmaters

$$xe^{-1/y}=0.6$$ and $$xye^{-1}=1.2$$

I am trying to solve this equations for approximate value of the parameters $x$ and $y$ using SageMath. any help would be appreciated.

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What did you try?

( 2017-04-07 02:06:47 -0500 )edit

## 1 answer

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The two equations allow a quick elimination of $x>0$. We can than numerically solve the remaining one equation in the remaining single variable $y$. The following code may help to get the relevant information, adapted to my taste:

sage: f(y) = log(y) +1/y -1 - log(2)
sage: f
y |--> 1/y - log(2) + log(y) - 1
sage: plot( f, 0.2, 0.5 )
Launched png viewer for Graphics object consisting of 1 graphics primitive
sage: find_root( f, 0.2, 0.4 )
0.3733646177016173
sage: gp( "solve( y=0.2, 0.4, %s )" %f(y) )
0.37336461770167408424844843667927059501


(The value for $x$ is easily found from the second equation.)

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Asked: 2017-04-06 20:39:11 -0500

Seen: 107 times

Last updated: Apr 07 '17