cancel out vs eliminate

cancel out and eliminate both are verbs.

Word	Noun	Adjective	Verb	Adverb
cancel out	No	No	Yes	No
eliminate	No	No	Yes	No

As verbs, eliminate is a hypernym of cancel out; that is, eliminate is a word with a broader meaning than cancel out:

Other hypernyms of cancel out include do away with, extinguish, get rid of.

cancel out (verb)	eliminate (verb)
wipe out the effect of something	eliminate from the body
	kill in large numbers
	terminate, end, or take out
	remove (an unknown variable) from two or more equations
	dismiss from consideration or a contest
	remove from a contest or race
	get rid of something