       Re: System for which Solve and NSolve both fail

• To: mathgroup at smc.vnet.net
• Subject: [mg30580] Re: [mg30572] System for which Solve and NSolve both fail
• From: BobHanlon at aol.com
• Date: Thu, 30 Aug 2001 03:51:26 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```In a message dated 2001/8/29 2:11:11 AM, ben at spam.bugs.me.quickmath.com
writes:

>I noticed that Mathematica seems unable to solve this system of equations
>:
>
>3^x + 3^y = 90
>
>x + y = 6
>
>With a bit of thought, you can see by inspection that the solutions are
>
>{x , y} = {2 , 4} or {4 , 2}
>
>However, when I use the commands
>
>Solve[{3^x+3^y==90,x+y==6},{x,y}]
>
>or
>
>NSolve[{3^x+3^y==90,x+y==6},{x,y}]
>
>I get a warning message starting with
>
>Solve::incnst: Inconsistent or redundant transcendental equation
>
>Can anyone shed some light on what is going on here? Any way to get around
>this problem?
>

Needs["Graphics`ImplicitPlot`"];

Needs["Graphics`Colors`"];

Solve and NSolve are primarily for polynomial equations.  Use FindRoot

eqns = {3^x + 3^y == 90, x + y == 6};

ImplicitPlot[eqns, {x, 1, 5}, {y, 1, 5}, PlotStyle -> {Red, Blue}];

FindRoot[eqns, {x, 4.1}, {y, 2.2}] // Rationalize[#, 1*^-8]&

{x -> 4, y -> 2}

FindRoot[eqns, {x, 2.2}, {y, 4.1}] // Rationalize[#, 1*^-8]&

{x -> 2, y -> 4}

eqns /. {%, %%}

{{True, True}, {True, True}}

Bob Hanlon
Chantilly, VA  USA

```

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