A parking lot has 66 vehicles (cars, trucks, motorcycles and bicycles) in it. There are four times as many cars as trucks

Let c, t, m, b denote the number of cars, trucks, motorcycles, and bicycles. Then the statements from the problem yield the equations:

c + t + m + b = 66

c − 4t = 0

4c + 4t + 2m + 2b = 252

We form the augmented matrix for this system and row-reduce

The first row of the matrix represents the equation c = 48, so there are 48 cars. The second row of the matrix represents the equation t = 12, so there are 12 trucks. The third row of the matrix represents the equation m + b = 6 so there are anywhere from 0 to 6 bicycles. We can also say that b is a free variable, but the context of the problem limits it to 7 integer values since you cannot have a negative number of motorcycles.