Final Answer:
The equations that should be entered into a graphing calculator to find how many of each type of commercial is played are: 0.5x + y = 13 and x + y = 16.
Step-by-step explanation:
Let x represent the number of 30-second commercials and y represent the number of 60-second commercials. The total commercial time of 13 minutes (or 780 seconds) translates to 0.5x + y = 13, considering that each 30-second commercial contributes 0.5x to the total time.
Additionally, the total number of commercials played in an hour is 16, leading to the equation x + y = 16, as the sum of both types of commercials equals the total count of 16 commercials.
These equations can be solved simultaneously using a graphing calculator by plotting the two equations on the same graph to find the intersection point, which represents the values of x and y, i.e., the number of 30-second and 60-second commercials played, respectively.
Understanding how to set up and solve equations based on given conditions is crucial for solving problems involving unknown quantities, allowing for effective use of mathematical tools like graphing calculators.