Inequalities and Systems of Inequalities in Two Variables

Question

A family plans to spend two 8-hr days at Disney World and will split time between the Magic Kingdom and Epcot Center. Let x represent the number of hours spent at the Magic Kingdom and let y represent the number of hours spent at Epcot Center.

a. Set up two inequalities that indicate that the number of hours spent at the Magic Kingdom and the number of hours spent at Epcot cannot be negative.

b. Set up an inequality that indicates that the combined number of hours spent at the two parks is at most 16 hr.

c. Graph the solution set to the system of inequalities.

Answer 1

a. To show that the number of hours spent at each theme park cannot be negative,

we simply write two different inequalities (1 for each)

-x for hours spent at Magic Kingdom  -y for hours spent at Epcot Center

 

x>0 and y>0

 

b. One inequality to show the hours spent at both parks should be at most 16,

this means the combination of x and y must be less than or equal to 16. 

I apologize, there is no way for me to show the proper inequality symbol, 

but please note that this should be the "less than or equal to" symbol)

 

x+y</16

 

c. To graph, plot points to find the coordinates of all 3 lines. (Using x-intercepts, y-intercepts, slope or a table of x and y values). Test the point (0,0) for all 3 equations, meaning take the points x=0 and y=0 and plug in to the equation. If the statement that follows is true, such as 0</16, then shade the side of the line that has the point (0,0). Note: This may only apply for the 3rd equation in this case. Shade the proper sides of the 1st two equations, meaning the positive values of x and y. The areas that end up being overlapped with shading a total of 3 times is the area containing your answer.