Question

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? Thanks!

Answer 1

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