Ok, I am having trouble completing the following problem:

The flow of traffic (in vehicles per hour) through a network of streets is shown in Figure 1.16 (my attachment).

(a) Solve this system for

(b) Find the traffic flow when

(c) Find the traffic flow when

Ok, I am having trouble with part a. I feel once I get part a, parts b and c should be a fairly straightforward, plug in the values and go from there. Using my figure I get the following Input = Output equations for the labeled junctions in my figure:

Anyhow, when I put it into matrix form and proceed to RREF I get:

Because of the zero row I know

and

are free variables, so I set

and

. It's at this point I get stuck. I have tried to solve it, but I wind up getting an expression for

in both

and

. Do I need to let another variable be a free variable? Thanks for any and all help.