eliminate and difference with Mathematica ?

Hello all,

I am new here (I just installed Maxima). I want to replace Wolfram 
Mathematica for simple tasks because of lack of licenses. My usage is 
mostly in digital filters design, working with equations in Z-domain etc.

So I tried to to use following:
(C7) eliminate([Yn = C0*I0 + C1*I1 + C2*I2, I2 = I3 - k1*I2/z, I3 = Xn - 
k0*I1/z, I1 = I2/z + k1*I2, I0 = I1/z + k0*I3],[I0,I1,I2,I3]);
First I found that Maxima does not understand simple Y = k X ( or does 
it ? I need to input Y = k*X). Anyway it prints the results with this 
fashion(therefore no simple copy/paste possibility).

But the main problem is that after "eliminate" it prints a lot of stuff 
(about 20 lines) which I don't understand how to use it.

How can I simply get Mathematica's Yn ( ...) = Xn ( ...) ?

Thanks,
Vasek