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Re: System for which Solve and NSolve both fail

• To: mathgroup at smc.vnet.net
• Subject: [mg30578] Re: System for which Solve and NSolve both fail
• From: "Stephen P Luttrell" <luttrell at signal.dra.hmg.gb>
• Date: Thu, 30 Aug 2001 03:51:24 -0400 (EDT)
• Organization: Defence Evaluation & Research Agency
• References: <9mi1rt$54r$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

"Ben Langton" <ben at spam.bugs.me.quickmath.com> wrote in message
news:9mi1rt$54r$1 at smc.vnet.net...
> Hi,
>
> I noticed that Mathematica seems unable to solve this system of equations
:
>
> 3^x + 3^y = 90
>
> x + y = 6
>
>...

You could try the following type of approach:

1. Use ImplicitPlot to see roughly where the solutions lie.

<< Graphics`ImplicitPlot`

ImplicitPlot[{3^x + 3^y == 90, x + y == 6}, {x, 0, 10}, {y, 0, 10}];

2. Use FindRoot to accurately locate the solution(s), given approximate
starting point(s).

FindRoot[{3^x + 3^y == 90, x + y == 6}, {x, 2.5}, {y, 1.5}]

and

FindRoot[{3^x + 3^y == 90, x + y == 6}, {x, 1.5}, {y, 2.5}]


--
Stephen P Luttrell
QinetiQ, Malvern, U.K.