Each number on the diagram represents the average number of cars per day entering (blue) or leaving (red) these one-way streets. The arrows indicate the direction of traffic flow. NCDOT aims to model the hourly traffic flows along these roads as part of their plans to update the current traffic control measures (stop signs, traffic lights, etc.) at the intersections. Define x, u, v, and z to be the traffic flow in cars per day between intersections along Jones St., Wilmington St., Edenton St., and Salisbury St.,respectively. Furthermore, define y to be the total cars per day exiting the intersection of Jones St. and Wilmington St. to the east along Jones St. (a) [10 points] Identify the constraints in this problem, and use them to set up a system of linear equations that describes the traffic flow along each street. Your answer should include: i. A list of constraints along with an explanation for each constraint. ii. The linear system of equations that models this scenario. (b) [5 points] Use the Gauss-Jordan reduction method to solve the linear system obtained in part (a). Your answer should include: i. An augmented matrix representation of the system of equations in part (a). ii. The final augmented matrix obtained after applying the Gauss-Jordan reduction method. iii. The solution to the linear system. (c) [5 points] Use Google Maps, a physical map, or your personal experience/intuition to carefully examine the set of intersections under consideration. Then answer the following: