# Why can't Mathematica solve this system of equations?

I am trying to solve the following system of equations for three unknowns Theta, Nu, and K. All the other parameters are constants. The third argument in Solve, {ub, uc, pm}, is to be eliminated: i.e. I don't want the solution to contain ub, uc, or pm.

system = { Subscript[p,m] == K (Pi (c + uc)^2 - Pi (b + ub)^2)/(Pi c^2 - Pi b^2) ,
ub == (b (-2 a^2 Subscript[p,i] + (-b^2 (-1 + ν) + a^2 (1 + ν))
Subscript[p,m]))/((a^2 - b^2) θ) ,
uc == (c ((c^2 (-1 + ν) - d^2 (1 + ν)) Subscript[p,m] + 2 d^2
Subscript[p,o]))/((c^2 - d^2) θ) } // FullSimplify

Solve[system, {θ, ν, K}, {ub, uc, Subscript[p,m]}]


With the code as it stands, my Mathematica 9 just hangs. I have also tried Reduce. Could you please help me find what's wrong with my Mathematica code or identify the fault with the logic of how I posed the question? Thank you very much.

• You have system of 3 equations. How can you simoultaniously solve it for 3 variables and eliminate 3 more variables? In other words, if you eliminate ub, uc, pm, there is no equation to solve left... – bcp Mar 3 '14 at 10:34
• @rm -rf Actually what bcp wrote strikes me as fine for a response to this. It states in effect "You cannot do this, and here's why...". While such remarks are also fine for comments, I don't see how this query will get a viable response of a substantially different nature, and it is good to have at least one response posted. – Daniel Lichtblau Mar 3 '14 at 15:45
• @DanielLichtblau Thanks for contacting me. bcp's answer was flagged by another top user as "not an answer". The version of the answer that was flagged and deleted read more as a comment (the Solve part was added later), so I converted it to one. I've undeleted the answer now. Often, such answers generally point to a non-Mathematica related problem with the question and are usually closed. BTW, I did not get your ping... I was notified of this by Szabolcs. To reach me, it is better to ping me in an answer of mine or in chat :) – rm -rf Mar 3 '14 at 20:56
• @DanielLichtblau What rm means is that pings won't go through unless the pinged person has also commented on the same post. – Szabolcs Mar 3 '14 at 21:57

You have a system of 3 equations. How can you simultaneously solve it for 3 variables and eliminate 3 more variables? In other words, if you eliminate ub, uc, pm, there is no equation left to solve...
Solve[system, {θ, ν, K}]