Graphing and Interpreting Systems of Equations Quiz

1. A farmer has 100 meters of fencing to create a rectangular pen for his animals. If the length of the pen is represented by the equation y = 50 - x, where x is the width, graph the system of equations and find the intersection point. What does this point represent in the context of the problem?

• The intersection point is (10, 40), showing an unbalanced width and length for the pen.

• The intersection point is (25, 25), representing the optimal width and length of the pen.

• The intersection point is (50, 0), representing the maximum area of the pen.

• The intersection point is (0, 50), indicating the total length of fencing used.

2. A school is planning a field trip and has a budget of $300. The cost per student is represented by the equation y = 20x, where x is the number of students. If they also have a fixed cost of $100 for the bus, represented by the equation y = 100, graph the system and interpret the intersection point.

• The intersection point is (10, 200).

• The intersection point is (3, 60).

• The intersection point is (5, 100).

• The intersection point is (7, 140).

3. A company produces two types of gadgets. The profit from the first type is represented by the equation y = 15x, and the profit from the second type is represented by y = 10(20 - x). Graph the equations and find the intersection point. What does this point indicate about the production of gadgets?

• The intersection point is (8, 120), indicating optimal production levels for maximum profit.

• The intersection point is (0, 0), indicating no profit from either gadget.

• The intersection point is (5, 75), indicating a loss in production.

• The intersection point is (10, 150), indicating overproduction of gadgets.

4. A local gym offers two membership plans. The first plan costs $30 per month, represented by the equation y = 30x. The second plan has a one-time fee of $100 and costs $20 per month, represented by y = 20x + 100. Graph the system and determine the intersection point. What does this point signify?

• The intersection point is (8, 240).

• The intersection point is (15, 450).

• The intersection point is (5, 150).

• The intersection point is (10, 300).

5. A city is planning to build a park and has two options for the area. The first option is represented by the equation y = 2x + 10, and the second option is y = -x + 50. Graph the equations and find the intersection point. What does this point tell you about the area of the park?

• The intersection point is (40/3, 110/3), indicating where both park options provide the same area.

• The intersection point is (0, 50), meaning the second option is the only viable choice for the park.

• The intersection point is (10, 20), suggesting the park area is equal to the first option only.

• The intersection point is (20, 30), indicating the park will be larger than both options.

6. A restaurant sells two types of sandwiches. The first type has a price represented by the equation y = 5x, and the second type has a price represented by y = 3x + 10. Graph the system and interpret the intersection point. What does this point represent in terms of sales?

• The intersection point (5, 25) represents selling 5 sandwiches at a price of $25 for both types.

• The intersection point (10, 50) represents selling 10 sandwiches at a price of $50 for both types.

• The intersection point (3, 15) represents selling 3 sandwiches at a price of $15 for both types.

• The intersection point (0, 10) represents selling 0 sandwiches at a price of $10 for both types.

7. A charity event is selling tickets for two different seating options. The first option costs $15 per ticket, represented by y = 15x. The second option has a base cost of $50 plus $10 per ticket, represented by y = 10x + 50. Graph the equations and find the intersection point. What does this point indicate about ticket sales?

• The intersection point is (15, 225), indicating the second option is cheaper at higher quantities.

• The intersection point is (20, 300), indicating both options are sold out at that point.

• The intersection point is (10, 150), indicating both options yield the same revenue at 10 tickets sold.

• The intersection point is (5, 75), indicating the first option is more profitable.

8. A car rental company charges a flat fee of $50 plus $0.20 per mile driven, represented by y = 0.2x + 50. Another company charges $30 plus $0.25 per mile, represented by y = 0.25x + 30. Graph the system and interpret the intersection point. What does this point mean for customers?

• The intersection point is (80, 66), meaning both companies charge $66 for 80 miles driven.

• The intersection point is (60, 50), meaning both companies charge $50 for 60 miles driven.

• The intersection point is (100, 70), meaning both companies charge $70 for 100 miles driven.

• The intersection point is (90, 80), meaning both companies charge $80 for 90 miles driven.

9. A bookstore sells two types of books. The first type is represented by the equation y = 12x, and the second type is represented by y = 15 - 3x. Graph the equations and find the intersection point. What does this point represent in terms of book sales?

• The intersection point is (0, 15), representing no books sold and $15 revenue from the first type.

• The intersection point is (3, 9), representing 3 books of the second type sold and $9 revenue from the first type.

• The intersection point is (2, 24), representing 2 books of the first type sold and $24 revenue from the second type.

• The intersection point is (1, 12), representing 1 book of the second type sold and $12 revenue from the first type.

10. A tech company produces two models of laptops. The first model has a production cost represented by y = 500 + 200x, and the second model has a cost represented by y = 300 + 300x. Graph the system and interpret the intersection point. What does this point indicate about the production costs?

• The intersection point is (20, 4500), indicating both models have the same production cost at 20 units.

• The intersection point is (25, 5000), indicating the second model has a higher production cost.

• The intersection point is (30, 6000), indicating both models are produced at a loss.

• The intersection point is (10, 4000), indicating the first model is cheaper.