Lineage, System
The lineage radical and the lineage kanji are the same. Sometimes this kanji can also mean system. I guess a lineage is a kind of system, if you think about it.
Basically, think of 系 as linking things that belong together in some kind of group. Lineages, solar systems, genres, styles… Anything along those lines.
けい
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You trace your lineage back through your whole family system and realize every single relative loved cake (けい). Most of them were cake bakers too!
You come from a lineage of cake makers and eaters. No wonder you love cake so much! (And if you hate cake, no wonder your family doesn't like you.)