In this lesson a real water supply network problem is analysed. First, we identify the unknowns and the equations and explain their physical and engineering meaning. Later, we write system of linear equations in matrix form, discussing the importance of the node and unknown numbering in the matrix banded structure. Next, we find that the compatibility condition is a flow balance equation. Finally, we find the general solution as the sum of a linear space with dimension equal to the numnber of holes in the network, which base can be immediately determined, and finally, a particular solution is obtained, so that, there is no need of a computer to find the gneral solution of the resulting system of linear equations.