I am learning about Network Analysis in Linear Algebra and I need help figuring out how to get the equations from this graph:
The arrows represent how many particles are going in a given direction.
The back of the book tells me they are:
$$x_1 + x_2 = 20$$ $$x_3 + 20 = x_4$$ $$x_2 + x_3 = 20$$ $$x_1 + 10 = x_5$$ $$x_5 + 10 = x_4$$
From my understanding, if we look at first equation, there are twenty particles going to the $1$ and they can split in two directions. So if you add up $x_1$ and $x_2$, they should equal twenty as it is impossible to go higher than that.
Even if I am correctly analyzing the first equation, I don't understand the rest of the equations that the book gives. For example, how does $x_3 + 20 = x_4$? What do $x_3$ and $20$ have to do with $x_4$?
Any help would be appreciated. Thank you!