Let x be the number of hours spent at the waterpark, and y be the number of hours spent at the mall. Then, the system of inequalities that represents the situation is:
x + y ≤ 10 (total time cannot exceed 10 hours)
x > 5 (time spent at the waterpark must be more than 5 hours)
y > 2 (time spent at the mall must be more than 2 hours)
Graphically, this system of inequalities represents a shaded region in the first quadrant of the xy-plane that is bounded by the x-axis, y-axis, the line x + y = 10, and the line x = 5. The shaded region is the feasible region, or the set of all possible combinations of x and y that satisfy the constraints.
One example of the amounts of time that can be spent at the locations is x = 7 hours at the waterpark and y = 3 hours at the mall. This satisfies all the constraints:
7 + 3 = 10 (total time is less than or equal to 10 hours)
7 > 5 (time spent at the waterpark is more than 5 hours)
3 > 2 (time spent at the mall is more than 2 hours)
Graphically, this point (7, 3) lies inside the feasible region.