Deriving the coefficient of restitution formula

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GreenSabbath
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http://upload.wikimedia.org/math/5/c/b/5cbdceba601a68315f744dc1c06e9ba7.png"
How wxactly has this equation be derived?

http://upload.wikimedia.org/math/3/c/5/3c53f3d1c66725053decc7e3e546c32d.png"
Can someone help me with the derivation. I can't trace the orgin of the second part od the systems of equation.

Help needed urgently Thanks
 
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Not clear what your question is. Those two equations in your second link:
(1) Looks like conservation of momentum (OK)
(2) Looks like "c" is the coefficient of restitution (not quite right)

You'll have to fix the second equation. It should read:
[tex]V_{1f} - V_{2f} = c(V_2 - V_1)[/tex]

Then, to combine those equations to get the equation in your first link: multiply the 2nd equation by M2 and add it to the first equation. Isolate V1f.
 
You derive it by perseverance.
Solve the linear system of equations you are supposed to solve.

If you don't have the skill to solve a system of linear equations, that is what you should focus on.

If you can't be bothered to perform the operations yourself, there is no reason for us to help you out, is there?