Momentum is conserved for all interactions elastic, partially elastic, totally inelastic, or even where energy is added, as in the case of fusion reactions or collisions with overinflated 400 kg women ( if you weren't there 9th period Tuesday you won't understand.... and its better that way).
Elastic simply means total KE before = Total KE after. Totally inelastic is often used to mean the objects stick together.
However sometimes we choose to divide the interacting objects into" the system" and the external world as a matter of convenience. In those cases the net impulse from the external forces produce a change in the total momentum of the system: delta psystem = Jnet from external sources. If a system consists of 2 objects what one loses, the other gains.
Remember direction matters backwards = - forwards and x and y must be treated separately.
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