The following diagram shows a network of one$-$way streets with traffic flowing in the directions indicated. The flow rates along the streets are measured as the average number of vehicles per hour.

$($a$)$ Set up a linear system whose solution provides the unknown flow rates.

$($b$)$ Solve the system for the unknown flow rates.The following diagram shows a network of one$-$way streets with traffic flowing in the di$-$ rections indicated. The flow rates along the streets are measured as the average number of vehicles per hour.