       Re: Re: System for which Solve and NSolve both fail

• To: mathgroup at smc.vnet.net
• Subject: [mg30820] Re: [mg30578] Re: System for which Solve and NSolve both fail
• From: Richard Gass <gass at physics.uc.edu>
• Date: Wed, 19 Sep 2001 00:17:16 -0400 (EDT)
• References: <9mi1rt\$54r\$1@smc.vnet.net> <200108300751.DAA01707@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Another approach is to use Eliminate.
eqn = {3^x + 3^y == 90, x + y == 6}

In:=
Eliminate[eqn,x]

From In:=
Eliminate::ifun: Inverse functions are being used by Eliminate, so some \
solutions may not be found.

Out=

y
Log[90 - 3 ]
------------ == 6 - y
Log

In:=
Solve[%,y]

From In:=
Solve::ifun: Inverse functions are being used by Solve, so some solutions may \
not be found.

Out=
{{y\[Rule]2},{y\[Rule]4}}

>"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
>>
>>...
>
>"Stephen P Luttrell" <luttrell at signal.dra.hmg.gb>  wroteYou 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.

--
Richard Gass
Department of Physics
University of Cincinnati
Cincinnati, OH 45221
phone- 513-556-0519
E-Mail gass at physics.uc.edu

```

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