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Re: NEWBIE: How do I use the results of a Solve?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg95994] Re: NEWBIE: How do I use the results of a Solve?
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Sat, 31 Jan 2009 06:44:35 -0500 (EST)
  • Organization: The Open University, Milton Keynes, UK
  • References: <gm0q3d$rm2$1@smc.vnet.net>

In article <gm0q3d$rm2$1 at smc.vnet.net>, Tim Heger <timheger at yahoo.com> 
wrote:

> I can't figure out how to use the results of Solve I just created  as a new
> variable.
> 
> Here's a simple example of what I am trying to do:
> 
> Solve[some equation, x]
> 
> Results in {x->12}
> 
> I then want to use the x in  y =  x * 5 for example....
> 
> Obviously when I try to use this it fails because Mathematica sees the
> equation as y = {x->12} * 5  and not y = 12 *5 ...
> 
> How do I change the results from the Solve from a rule to an actual value I
> can then use?

The function Solve returns a list of transformation rules (possibly an 
empty list or just one) that can be further applied to other expressions 
via the replacement operator /. as you can see in the following examples:

In[1]:= sol = Solve[x - 12 == 0, x]

Out[1]= {{x -> 12}}

In[2]:= y = x*5 /. sol[[1]]

Out[2]= 60

In[3]:= sol = Solve[x^2 - 12 == 0, x]

Out[3]= {{x -> -2 Sqrt[3]}, {x -> 2 Sqrt[3]}}

In[4]:= y = x*5 /. sol

Out[4]= {-10 Sqrt[3], 10 Sqrt[3]}

The tutorial "Solving Equations" might be worth reading. It is available 
on the web at

http://reference.wolfram.com/mathematica/tutorial/SolvingEquations.html

or directly from within the documentation center at 

tutorial/SolvingEquations

Regards,
--Jean-Marc


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