I think it would be nice if this could be called with rewrite in some
way so you could say `rewrite(Eq(y, x**2+4*x+10), Eq((x-h)**2 - 4*p*(y-
k), 0), match=[x, y]) -> {p: 1/4, h: -2, k: 6}`.

'Eliminate' is not so descriptive to me...the real-world phrase I
would say is "rewrite THIS as THAT matching THESE constants". And that
is your point, I think: solve should be able to handle that. What was
not subtle in the first example and in this one is that the variables
to be solved for are all in one equation and everything else in the
other equation appears in the 2nd equation.

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