Does anyone understand exactly what is going on in the example and how to use it for the next two problems? can anyone explain this value substitution method? !

From the looks of it, it is just smart substitution.  Basically, you want to pick values for "x" in such a way that one of the variables disappear.  Do this enough times and you can get a solvable set of equations.

So for (2)
Pick x = 1 (doing this removes the a variable)
We get:
4b + c = 1

Now pick x = -1 (doing this removes the b variable)
We get: 
4a + c = 1

Now there is no way to remove the c variable so let's just pick x = 0. 
We get:
a + b + c = 0

Now we have 3 set of equations and 3 variables.

Solve this by using Gauss-Jordan elimination or whatever other technique you know (Or just use an online matrix calculator).

You should get:
a = 1/2
b = 1/2
c = -1

Set up a system of equations