系 has two readings: xì (system / department / relation — the everyday meaning, found in 系统, 关系, 系列) and jì (to tie / fasten, used in 系鞋带 'tie shoelaces' and 系安全带 'fasten seatbelt'). The simplified form merges three traditional characters: 系, 係, and 繫 — all written as 系 in the mainland.
memory
Picture a hand reaching down to a silk skein — that is the graph of 系. From 'tying threads together' grew the abstract senses of linking, connecting, and finally 'system'. The original physical act of tying lives on in the jì reading.
The silk-skein radical, indexing component for 系. It pictures twisted silk threads with a knot at the top. Combined with the hand stroke above, the whole graph reads 'a hand tying the thread' — origin of the senses 'connect, link, system, tie.'
A leftward downstroke at the very top representing a hand reaching down to grasp the silk below. This abbreviated hand-graph is what distinguishes 系 from plain 糸: it shows someone tying or attaching the thread, not just the thread itself.