Samyoga is the dualistic doctrine of Samkhya and Yoga. It recognizes two eternal basic realities underlying the universe, namely, purusha (the self) and prakriti (primordial nature). As Prakriti is instituted by three gunas and the self is totally devoid of them, there can really be no relation between them. To solve this difficulty the dualistic take recourse to samyoga (the notion of togetherness).
Patanjali has said in yoga sutra (II.16-17) that suffering in the life of an individual (heya) is caused by Samyoga between the atma and the world. Samyoga is said to be beginningless but not endless (eternal) like the two basic realities. When ignorance is dispelled by the rise of self-knowledge, samyoga comes to an end, (II.24), which is called the state of hana, e.e., the kaivalya (liberation) of the atma (II.25).
In Samkhya Karika (20) also samyoga is taken for granted. It causes superimposition of the characteristics of purusha and prakriti (or rather buddhi) on each other. So buddhi appears to be sentient (cetanavadiva), and the purusha appears as an agent (karta) (karteva bhavati udasinah). The purpose of the samyoga is said to be the self-realization of purusha and isolation to the pradhana (Samkhya Karika 21). As explained in karika 65 and 66, by self knowledge the purusha becomes a mere observer, and prakriti retires from creation, and the purusha is never bound again, the state of kaivalya never being disturbed.