# Solving three simultaneous equations for analytical solution

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Teck Lim on 16 Mar 2020
Commented: Teck Lim on 16 Mar 2020
Hi there, I am trying to solve for k_t+1, tau_t, l^t-1_2 in terms all other parameters that are taken to be given. You can assume that w(h_t)=exp(bh_t). I have tried executing this code:
syms k2 k1 R B s h a l2 l1 t1 t2 b d
[solk2,solt1,soll2]=solve(k2==(BR(exp(bh)(1-l2-a)-t1)-t2)/(BR+R),t1==(d(exp(bh)(1-l2-a)-k2)-Rk1)/(1+d),l2==(s(exp(bh)(1-a)-k2-t1))/(exp(bh)+sexp(bh)))
I am getting the error message Indexing with parentheses '()' must appear as the last operation of a valid indexing expression.
What should I change in the code to run it properly?

Stephan on 16 Mar 2020
Keep it short and simple + use "*" for multiplication operations:
syms k2 k1 Rk1 R BR s h a l2 l1 t1 t2 bh d
eq(1) = k2==(BR*(exp(bh)*(1-l2-a)-t1)-t2)/(BR+R);
eq(2) = t1==(d*(exp(bh)*(1-l2-a)-k2)-Rk1)/(1+d);
eq(3) = l2==(s*(exp(bh)*(1-a)-k2-t1))/(exp(bh)+s*exp(bh));
vars = [k2, t1, l2]
[solk2,solt1,soll2]=solve(eq,vars)
Im not sure what you want to do with this code, because the solution for k2, t1 and l2 are already there in the equations.

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Teck Lim on 16 Mar 2020
I tried the code and it works out fine. Thanks!
Now that I have solved for k2,t1 and l2 in terms of parameters, I want to solve for E and F in the following equation by subbing in the optimal k2, t1, and l2 that I just found on the right hand side. Does this seem like something that can be coded on MATLAB?
Stephan on 16 Mar 2020
You might want to use subs.
Teck Lim on 16 Mar 2020
Alright, thank you