Systems of Linear Equations in Vehicles

In a town, the number of bicycles and cars is such that for every 3 bicycles, there is 1 car. The total number of vehicles (bicycles and cars combined) is 160. If the number of cars can be represented as $c$ and the number of bicycles as $b$, which of the following systems of equations correctly represents this situation?

The equations should express that the relationship between bicycles and cars is maintained, and the total vehicles adds up to 160. Use the following relationships:

1. The ratio of bicycles to cars: $b = 3c$.

2. The total number of vehicles: $b + c = 160$.