Oh boy, the F word.

Feudalism isn't really a "thing" as we understand political-economic systems from a modern standpoint, it's a name we've projected backwards as an umbrella for a whole series of power structures, economic relationships, interpersonal relations, mutual agreements and the like. You can read a really good post on the historiography of Feudalism by /u/Miles_sine_Castrum here.

'Feudalism' at its core is a series of overlapping mutually beneficial relationships based on the exchange of land, service and authority. A king agrees to lease land to a noble in return for his loyalty and his service and/or his taxation. That noble in turn leases to a lieutenant, in response for his service, and so on. Eventually, a manorial lord agrees to lease land to tenant farmers from the peasantry: they provide him with rent, usually in the form of service obligations carried out on manorial land or as food render, and in return they gain land on which to raise a family and from which to draw an income, legal and (in extremis) military protection, and access to communal services. Of course, in practice, things are not always this clear cut; things are muddled by all kinds of other relationships, freemen, the Church, enterprising Marcher lieutenants, towns and so forth. Slavery had always had more of a 'do what I say or I'll kill you' vibe.

The two practices are far from mutually exclusive; slavery existed alongside 'feudal' peasantry in England until the 12th Century, for example, and a series of definite legal boundaries distinguished the rights of free men from those of slaves.