Question:
A bus of mass 1400kg that is traveling West, collides with a small truck of mass 900kg that is traveling North. As a result of the collision, the two trucks join together. A cop determines from the skid marks that the immediately following the collision the joint trucks moved at 12m/s in the direction 37 degrees west of north. Calculate the initial velocity of both trucks.

Attempted Solution:
I started by setting up two equations: one for the x component and one for the y component.

x: m1v1x + m2v2x = (m1+m2)ux --> (1400)(v1x) + (900)(v2x) = (1400+900)(12cos37)
y: m1v1y + m2v2y = (m1+m2)uy --> (1400)(v1y) + (900)(v2y) = (1400+900)(12sin37)

Now I'm stuck. I have two equations with four variables.. Where do I go from here?

(Note: I know that the answer is 11.9m/s and 24.5m/s, but can't figure out how to get there)

Remember that initially the 1400 Kg vehicle is traveling due west, so v1y = 0. And the 900 Kg vehicle is initially traveling due north, so v2x = 0. Now you have two equations in two unknowns. And by the way: you titled this problem "Elastic Collision - trucks," but this is NOT an elastic collision - its inelastic. If the crash was elastic the two vehicles would bounce off each other, rather than stick together.