A section of a citys street network is shown in the figure T

A section of a city\'s street network is shown in the figure. The arrows indicate one-way streets, and the and the numbers show how many cars enter or leave this section of the city via the indicated street in a certain one-hour period. The variables x, y, z, and w represent the number of cars that travel along the portions of First, Second, Avocado, and Birch Streets during this period. Find x, y, z and w, assuming that none of the cars stop or park on any of the streets shown. (If the system has infinitely many solutions, express your answer in terms of t, where x = x(t), y = y(t), z = z(t) and w = t. If the system is inconsistent, enter INCONSISTENT.) (x, y, z, w) = (____)

Solution

1 st corner : x +z = 140 + 290 = 430

2nd corner : x +90 = 50 +w

x-w = -40

3rd corner : y+z = 480 +260 = 740

4rt corner : w + 280 = y +10

w - y = -270

Solve the 4 equations we get : system has infinite solutions.

Let w = t

y = w +270 = t+270

x -w = -40 ; x= w -40 = t -40

x = t -40

x +z = 430

z = 430 -x = 430 -(t-40) = 470 -t

So, solution : (x , y, z, w) = ( t-40 , t+ 270 , 470 -t ,   t)