A ball at rest has no momentum.  It is in its state of inertia.  As stated in our definition, the law of conservation of momentum states that the vector sum of the momentum is constant.  That applies to closed systems. 

When Ball A is going to the right along the X axis it has momentum only in that direction.  For our purposes let's say that the momentum of Ball A is 5 m/s.  Ball B is in the path of Ball A.  Ball A hits Ball B and they move off in their respective angles.  Momentum is represented by mass x velocity.  If Ball A has a mass of 2kg the momentum is equal to 10 kgm/s.

Ball B also has a mass of 2 kg.  Dependent on the angle of Ball A are the angles at which both balls will roll.  Let's assume that Ball A will go off at 30 degrees and Ball B will go off at 60 degrees.  After they come in contact with one another both balls will have a y and an x component.  These components can be figured out with geometry.