Aaron S. Meurer wrote:
>> I don't know what Mathematica's Eliminate does, but it seems to me
>> that the solve() line below should just work, without the user
>> having to consider what kind of solving procedure is necessary to
>> solve it.   
>> 

It's more subtle than that: if I say that `a + 3*b = 0` and `a + c*b + d = 0` 
and I want to match coefficients keeping only c and d then I infer that `c, d = 
3, 0`. But if I were not matching coefficients then I could only infer that `d 
= b*(3-c)` and although the solution found before satisfies this, there are 
also other solutions like `c, d = 1, 4` when `b = 2`.

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