How to Solve two equations simultaneously?

Questions
,
1

Hello,

I’m trying to understand how to use Mathematica better, instead of plugging all of this into excel and using solver. I want to try to find the answers via Mathematica.
I have two equations:

fa = (0.3*100) - x - (x/25)^1.5*exp[14 - 500/T]*50 == 0  
ft = -(100) (16) (T - 350) - (-6000) (30 - x) == 0

    Solve[{fa,ft}, {T,x}]

did not get the result I needed. The answer for T should be around 453.8 and x = 2.30

The system gives me:

Solve::inex: Solve was unable to solve the system with inexact coefficients or the system obtained by direct rationalization of inexact numbers present in the system. Since many of the methods used by Solve require exact input, providing Solve with an exact version of the system may help.

Thank you,

2

Here is one method of finding a solution

sol=NMinimize[Abs[(0.3*100) - x - (x/25)^1.5*Exp[14 - 500/T]*50]+
  Abs[ -(100) (16) (T - 350) - (-6000) (30 - x)],{x,T},Method->"RandomSearch"]

which returns

{0.000541444,{x->0.00323301,T->462.488}}

And I inspect what each of your expressions are with those values

(0.3*100) - x - (x/25)^1.5*Exp[14 - 500/T]*50/.sol[[2]]

which returns

0.0000566773

and

(100) (16) (T - 350) - (-6000) (30 - x)/.sol[[2]]

which returns

0.000484766

Please check that carefully to make certain I haven’t made any mistakes.

3

Using Solve

fa = (0.3100) - x - (x/25)^1.5 Exp[14 - 500/T]*50 == 0
ft = -(100) (16) (T - 350) - (-6000) (30 - x) == 0

sol = Solve[{Rationalize@fa, ft}, {x, T}, Reals] // N
(* {{x -> 0.000153337, T -> 462.499}} *)

Verify

First@fa /. sol
(* {-1.52614*10^-11} *)
First@ft /. sol
(* {0.} *)
4

Thank you so much, that was very helpful.

However, my x value is incorrect but the T value is very close.

I’m assuming using solver on excel can get you a wide range of x depending on your initial input.

Thank you guys again. Really appreciated.

5

Thank you so much, that was very helpful.

However, my x value is incorrect but the T value is very close.

I’m assuming using solver on excel can get you a wide range of x depending on your initial input.

Thank you guys again. Really appreciated.

6

Hi Jason,

What value of x does the Excel solver give?

7

T = 453.826
x = 2.30

is what Excel gave me.

8

T = 453.826 x = 2.30

is what Excel gave me.

Really appreciated for your time.

9

Well, those values do not solve the equations. Both results should be close to zero.

First@fa /. {x -> 2.30, T -> 453.826}
(* -557564. *)

First@ft /. {x -> 2.30, T -> 453.826}
(* 78.4 *)

Most likely the equations you solved in Excel are not the same as the ones in your question. Perhaps a different constant or misplaced parenthesis? Please compare the equations and check that they are correct in the question.

10

you are correct, the value 500/T should be 5000/T.

Appreciated, thank you.

11

There is still a discrepancy using 5000/T, Solve gives

{{x -> 0.0823298, T -> 462.191}}