I have taken 2 10 milligram methadone pills last week how long will it stay in my system?

It depends: Methadone because it stays in the body's fat can remain detectable in the body for extended periods. Hair testing might show its presence for months. Most screening, however, is through urine and with standard cut-offs I would expect after a week it wouldn't come up as positive unless previous use was high or there was some significant problem effecting excretion.