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I have derived a set of equations of motion and now want to rearrange and simply them, but I am not sure which command I should use.

For example, I have:

d F_1 + e F_2 == M a; 
F_1 == m + n; 
F_2 == f + g; 
m == K + L;

Now I want to eliminate F_1, F_2, and m, since they are redundant. I tried Eliminate, but it gave me weird results when I had more than one set of such equations. What is the best command I should use to rearrange and simplify these equations?

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eqns = {d F1 + e F2 == M a, F1 == m + n, F2 == f + g, m == k + l};
Eliminate[eqns, {F1, F2, m}]

-e g - d k - d l + a M - d n == e f

Note: F_1 and F_2 are not appropriate variable names in Mathematica. (See Blank (_) in the docs.)

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