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In a perfectly inelastic collision the bodies move off together, so momentum conservation alone fixes the answer: v = (m1u1 + m2u2)/(m1+m2). Kinetic energy is not conserved - it goes into deformation, heat and sound. A 1200 kg car at 15 m/s hitting a 900 kg car at -5 m/s leaves the pair at 6.43 m/s, having destroyed about 51% of the kinetic energy.
Combined velocity
v = (m1 u1 + m2 u2) / (m1 + m2)
Energy lost
loss = KE before - KE after
Momentum conservation follows from Newton's third law and holds in every collision. Energy can hide as heat and deformation, which momentum cannot.
Close to it when the vehicles lock together. Crumple zones are designed to maximise energy absorption for exactly this reason.