If the net external force exerted on a system of colliding objects is zero, then the sum of the x- and y-components of momentum is conserved. For two-object systems

Momentum Before = Momentum After
m₁v_1ox + m₂v_2ox = m₁v_1x + m₂v_2x
m₁v_1oy + m₂v_2oy = m₁v_1y + m₂v_2y

If no work is done on a system involved in a perfectly elastic collision, then the kinetic energy of the system is conserved, that is constant. For two-object systems

Kinetic Energy Before = Kinetic Energy After
0.5m₁v_1o² + 0.5m₂v_2o² = 0.5m₁v₁² + 0.5m₂v₂²