##### Item1.3.5.2.a

How many cars per hour enter the upper left intersection? How many cars per hour leave this intersection? Use this to form a linear equation in the variables \(x\text{,}\) \(y\text{,}\) \(z\text{,}\) and \(w\text{.}\)

Form three more linear equations from the other three intersections to form a linear system having four equations in four unknowns. Then use Sage to find the solution space to this system.

Is there exactly one solution or infinitely many solutions? Explain why you would expect this given the information provided.