Two bumper cars in an amusement park ride collide elastically as one approaches

Question

Two bumper cars in an amusement park ride collide elastically as one approaches the other directly from the rear. one has a mass of 450 kg and the other 550kg, owing to differences in passenger mass. if the lighter one approaches at 4.5 m/s and the other is moving at 3.7 m/s, calculate:
a) their velocities after the collision and
b) the change in momentum of each

Can someone do part A using two equations (system of equations, not the relative velocity way), and show all work please

Like for a part of mine i get: (m1v1i + m2v2i - m2v2f)^2 so youhave to square that giving you nine terms so is there any other shorcuts that way i dont take forever on a test (like can you cancel things).

Explanation / Answer

a) v1 = 3.62 m/s v2=4. 42 m/s b)change of first= -396 mkg/s change of first = 396 mkg/s

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