How to solve elastic collision equations for v1' and V2'

[Super6]

Can anyone help show me the process of solving the equations
(m1*v1)+(M2*V2)=(m1*v1')+(M2*V2')
(.5m1*v1^2)+(.5M2*V2^2)=(.5m1*v1')+(.5M2*V2')

to get the equations

------(m1+M2) (2M2v)
v1'= --------- v1 + ----- V2
------(m1+M2) (m1+M2)


-------(2m1) (M2-m1)
V2'= --------- v1 + ----- V2
------(m1+M2) (m1+M2)


i need the algebra used or at least how i should start i know you solve one and plug it into the other, but I am not sure if i should start by factoring, expanding or what any help would be greatly appreciated

 

[mathman]

Your equations are full of typographical errors, so it is to understand what you are trying to get.

One hint: conservation of momentum is a VECTOR equation, so it is actually three equations in the three components of velocity. On the other hand, the energy equation is scalar, where the velocity magnitude squared appears.