A system and method for argon and nitrogen extraction and liquefaction from a low-pressure tail gas of an ammonia production plant is provided. The preferred tail gas of the ammonia production plant comprises methane, nitrogen, argon, and hydrogen. The disclosed system and method provides for the methane rejection via rectification and hydrogen rejection by way of a side stripper column or phase separator. The resulting nitrogen and argon containing stream is separated and liquefied in a double column distillation system.