Patrick T. answered • 11/27/21

Tutor Specializing in French & Math (up to college Pre-Calculus)

Hello Erika,

Let's call x the the number of hours

Let's call y the cost of parking:

For garage A, a $6 flat fee means you only pay that fee once. The $0.50 per hour means $0.50 is multiplied by whatever the number of hours is. Therefore the function that describes the parking cost for garage A is:

**y**_{A}** = 6 + 0.50x**

For garage B, a $2 flat fee means you only pay that fee once. The $1 per hour means $1 is multiplied by whatever the number of hours is. Therefore the function that describes the parking cost for garage B is:

**y**_{B}** = 2 + 1*x = 2 + x**

As you can tell from the two linear equations:

- the slope of the line for garage A is 0.5
- the slope of the line for garage B is 1

Because the slopes are different, the two lines will intersect exactly ONE time. In other words, ** the number of solutions is one (1)**.