simple Netwrok analysis

Networks composed of branches and junctions are used as models in many diverse fields
such as economics, traffic analysis, and electrical engineering.
In such models it is assumed that the total flow into a junction is equal to the total flow
out of the junction. For example, because the junction shown in Figure 1.9 has 25 units
flowing into it, there must be 25 units flowing out of it. This is represented by the linear
equation
x1+ x2 = 25.
Because each junction in a network gives rise to a linear equation, you can analyze
the flow through a network composed of several junctions by solving a system of linear
equations. This procedure is illustrated in Example 5.