# How to solve this system of equations?

**URL:** <https://community.wolfram.com/t/how-to-solve-this-system-of-equations/6277>\
**Category:** Questions\
**Tags:** equation-solving\
**Created:** [July 27, 2015, 12:45pm UTC](https://community.wolfram.com/t/how-to-solve-this-system-of-equations/6277 "2015-07-27T12:45:49Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![laurentsimula](https://avatars.discourse-cdn.com/v4/letter/l/f4b2a3/32.png) [@laurentsimula](https://community.wolfram.com/u/laurentsimula)\
**Post date:** [July 27, 2015, 12:45pm UTC](https://community.wolfram.com/t/how-to-solve-this-system-of-equations/6277/1 "2015-07-27T12:45:49Z")

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Hi!

I am trying to solve the system of equations in the attached file. What I am looking for are the values of tP and tC, both in (0,1), which satisfy:

exp3= tP/(1 - tP) and exp6 = tC/(1 - tC)

I am using FindRoot, but I have reasons to believe that it is not returning all the solutions. How would you solve this system of equations in Mathematica? Thanks a lot for your help.

Laurent

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**Author:** ![fkampas](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/fkampas/32/41217_2.png) [@fkampas](https://community.wolfram.com/u/fkampas)\
**Post date:** [July 27, 2015, 2:03pm UTC](https://community.wolfram.com/t/how-to-solve-this-system-of-equations/6277/2 "2015-07-27T14:03:12Z")

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FindRoot only gives one solution for a given starting point. If you want more solutions, you should try more starting points.

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**Author:** ![gianlucagorni](https://avatars.discourse-cdn.com/v4/letter/g/ec9cab/32.png) [@gianlucagorni](https://community.wolfram.com/u/gianlucagorni)\
**Post date:** [July 27, 2015, 2:29pm UTC](https://community.wolfram.com/t/how-to-solve-this-system-of-equations/6277/3 "2015-07-27T14:29:58Z")

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I have some doubts that there are more than one solution, at least in the unit square. The following plots show ony one likely candidate:

```
Plot3D[{Sqrt@Norm[{exp3 - tP/(1 - tP), exp6 - tC/(1 - tC)}], 0}, {tC, 
  0, 1}, {tP, 0, 1}, PlotRange -> {-.1, 1}, AxesLabel -> Automatic]
Plot3D[{Sqrt@Norm[{exp3 - tP/(1 - tP), exp6 - tC/(1 - tC)}], 
  0}, {tC, .8, .9}, {tP, 0.5, .9}, PlotRange -> {-.1, 1}]

```