Apply gauss method to a linear system and them use results in another system

Question

I have an exercise for my last assignment of linear algebra, which is the following:

I tried to row reduce to echelon form the matrix created by the first linear system of equations and I obtain this huge thing:

Which I don't know if it's correct or not. Is it correct?

Now, my problem is how would I apply what I have just found in the second linear of equations? Do I need to just replace for example $x$ with its value respect to $w$, $a$, $b$ and $c$, or what?

Answer 1

You solved the system with arbitrary parameters $a,b,c$. Now assume $a=12$, $b=1$, $c=2$.