The Collaborative International Dictionary of English v.0.48:

Elixate \E*lix"ate\, v. t. [L. elixatus, p. p. of elixare to
   seethe, fr. elixus thoroughly boiled; e + lixare to boil, lix
   ashes.]
   To boil; to seethe; hence, to extract by boiling or seething.
   [Obs.] --Cockeram.
   [1913 Webster]