Finding Final Velocity of Mass 1 After Collision

[Nicki]

Homework Statement

Mass 1 (2.77 kg) moves with an initial velocity (1i - 1j) and mass 2 (1 kg) starts at rest. After the collision, M2 moves with a velocity of (2i - 3j). What is the final velocity of m1?

Homework Equations

Since they don't stick together, KE and linear momentum are conserved.
M1V1ix + M2V2ix = M1V1fx + M2V2fx

M1V1iy + M2V2iy = M1V1fy + M2V2fy

1/2 M1V1i^2 + 1/2M2V2i^2 = 1/2 M1V1f^2 + 1/2M2V2f^2

V1f = (sqrt)V1xf^2 + V1yf^2

The Attempt at a Solution

I don't really understand these problems, and we had a substitute professor into teach this, so here goes nothing, literally.
2.77 (1) + 0 = 2.77 Vx + 1(2) Vx = 0.278 m/s ?
2.77(-1) + 0 = 2.77 Vy + 1(-3) Vy = 0.0.83 m/s ?

This doesn't seem right? Shouldn't I need to use th equations for KE for an elastic collision?

 

[haruspex]

Since they don't stick together, KE and linear momentum are conserved.

No. Momentum is conserved, but loss of some KE does not necessarily mean the objects coalesce. That is only the extreme case, in which the KE lost is maximised.