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