Let P1=13m/s(1250kg)=16250 kg m/s (positive velocity is north here)
P2=-19m/s(1250kg)=-23750 kg m/s
Total system momentum is P1 + P2 = 16250 - 23750 = -7500 (negative momentum is south pointing).
Due to the conservation of momentum, this is also the final momentum and we see the two cars have a mass of 1250 + 1250 = 2500kg and have a velocity
-7500 = 2500kg * Vfinal
Final = -3m/s (moving southward)
Each car's momentum changes from the initial value it had to this final value, but the total system momentum does not change, due to the conservation law.
