A B C and D are the four intersections in the diagram below

A, B, C, and D are the four intersections in the diagram below. Assume the incoming traffic and the outgoing traffic at a given intersection must be equal (to avoid pileups). Set up a system of linear equations which can be used to determine the values of x_1, x_2, x_3, and x_4. You do not have to solve your system of equations.

Solution

We assume

The # of cars arriving are equal to the # of cars which be leaving.

As you can look in the image all streets follows one way.

Variables are positive integers.

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Setting the system

Intersection A

x4 + 610 = x1 + 450

Intersection B

x1 + 400 = x2 + 640

Intersection C

x2 + 600 = x3

Intersection D

x3 = x4 + 520

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Checking the system

x4 - x1 = -160

x1 - x2 = +240

x2 - x3 = -600

x3 - x4 = +520

0 = 0

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Thus the system is useful for determining the variables.