I'm trying to solve a simple system of six equations and four variables, namely, $F,G,K$ and $L$. I need to solve the system for $F$ and $L$ in terms of $G$ and $K$,that is

$$ F(G,K) \,\, ,\\ L(G,K) \,\, , $$ but I don't have any idea of how can I command the Mathematica do it. Lately I'm using the command Solve to do that.

This is the system of equation that I'm treating with:

eq1=F + G == H + J

eq2=I F ω - I G ω == I H Sqrt[ω^2 - Subscript[V, 0]] - I J Sqrt[ω^2 - Subscript[V, 0]]

eq3=E^(I a Sqrt[ω^2 - Subscript[V, 0]]) H + E^(-I a Sqrt[ω^2 - Subscript[V, 0]]) J ==  E^(I a ω) K + E^(-I a ω) L

eq4=I E^(I a Sqrt[ω^2 - Subscript[V, 0]]) H Sqrt[ω^2 - Subscript[V, 0]] - I E^(-I a Sqrt[ω^2 - Subscript[V, 0]]) J Sqrt[ω^2 - Subscript[V, 0]] == I E^(I a ω) K ω - I E^(-I a ω) L ω

eq5=E^(I b ω) K + E^(-I b ω) L == 0

eq6=I E^(I b ω) K ω - I E^(-I b ω) L ω == 0

Thanks in advance!

  • 1
    $\begingroup$ In fact you want to find the solution of 6 equations with respect to 4 variables: F, L, ,J and H. The fact that you are not interested in the values of J and H plays no role. In this case, however, your system is over-determined. You only need 4 equations to do that. Then Solve will do the job. Note that K is reserved in Mma, you should not use it. $\endgroup$ – Alexei Boulbitch Aug 5 '16 at 8:50
  • $\begingroup$ @AlexeiBoulbitch, Thank you mate, I think that my problem now is with mathematics. Can you draft and solution for this problem? $\endgroup$ – Herr Schrödinger Aug 5 '16 at 8:58
  • $\begingroup$ No. As I explained above the mathematical statement of the problem is incorrect. I do not know, how to make a correct statement, since it depends on the problem you solve. You know this problem, while I do not. $\endgroup$ – Alexei Boulbitch Aug 5 '16 at 9:07
  • $\begingroup$ I'll edit the question to fix the mathematical statement. $\endgroup$ – Herr Schrödinger Aug 5 '16 at 9:09

I redefined the equations with lower cases.

eq = {eq1, eq2, eq3, eq4, eq5, eq6};

Solve[Eliminate[eq, l], f]

{{f -> -g + h + j}}

Solve[Eliminate[eq, f], l]

{{l -> -E^(2 I b \ω) k}}

| improve this answer | |
  • $\begingroup$ It didn't work, I need $F(G,K)$ and $L(G,K)$..... $\endgroup$ – Herr Schrödinger Nov 3 '16 at 14:26

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.