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Old English bycgan (past tense bohte) "to buy, pay for, acquire; redeem, ransom; procure; get done," from Proto-Germanic *bugjanan (cf. Old Saxon buggjan, Old Norse byggja, Gothic bugjan), of unknown origin, not found outside Germanic.
The surviving spelling is southwest England dialect; the word was generally pronounced in Old English and Middle English with a -dg- sound as "budge," or "bidge." Meaning "believe, accept as true" first recorded 1926. Related: Bought; buying. To buy time "prevent further deterioration but make no improvement" is attested from 1946.
"a purchase," especially a worthwhile one, 1879, American English, from buy (v.).
To accept; acquiesce in •Thought of and perhaps coined as the opposite of sell out, which has a more contemptuous suggestion of betrayal: lots of guilt and I bought into that/ I bought into the whole materialistic trip/ the degree with which you bought into the pop culture of the Fifties