This is the adverb of 'systematic': it tells you HOW something was done — in an organised, step-by-step way, following a method, leaving nothing out. 'They systematically checked every file' means they went through the files in order, one after another, until all were checked; not randomly, not just the interesting ones. Because it is an adverb, it usually sits next to the verb — before it ('she systematically removed'), or after the object ('she removed the names systematically'). It carries the same double life as 'systematic'. In academic and work writing it is a compliment: systematically tested, systematically recorded, systematically reviewed. But in news writing it very often introduces something ugly done deliberately over time — 'the evidence was systematically destroyed', 'villages were systematically burned'. In that second use the word is doing quiet, heavy work: it tells the reader this was policy, not chaos. One more practical note: 'systematically' is a favourite word of academic English. If you write research reports or read journal articles, you will meet it constantly, often with verbs like review, sample, exclude, compare and record.