extinguish, eliminate, get rid of, do away with -- (terminate, end, or take out; "Let's eliminate the course on Akkadian hieroglyphics"; "Socialism extinguished these archaic customs"; "eliminate my debts")
rule out, eliminate, winnow out, reject -- (dismiss from consideration or a contest; "John was ruled out as a possible suspect because he had a strong alibi"; "This possibility can be eliminated from our consideration")
excrete, egest, eliminate, pass -- (eliminate from the body; "Pass a kidney stone")
eliminate -- (remove from a contest or race; "The cyclist has eliminated all the competitors in the race")
eliminate -- (remove (an unknown variable) from two or more equations)