Lesson 6

Lesson 6: Solving Systems of Equations Algebraically

 

Focus

 

The World’s Fair of 1893 was an opportunity for the city of Chicago, Illinois, to showcase its architecture, technology, and the spirit of America. When the architects and designers were charged with the task of bringing the vision of a world’s fair to life, they were faced with the challenge of outdoing the World Exhibition of 1889, held in Paris to commemorate the centennial of the French Revolution. The Eiffel Tower was the centrepiece of the World Exhibition. Standing at 300 m, it became the undisputed tallest structure in the world, dwarfing the Washington Monument by twice the size.

 

In order to “out-Eiffel Eiffel,” and also to attract as many visitors as possible, the architects designed a lavish city within a city with magnificent buildings, exquisitely manicured landscapes, and the world’s first Ferris wheel. While the Ferris wheel did not rival the Eiffel tower in terms of height, reaching only 80.4 m (or approximately 27 storeys), the Ferris wheel was commanding in its own right. With a total of 36 cars, each of which could accommodate 60 people, the Ferris wheel could handle 2160 passengers!

 

The design and construction of an attractive and entertaining fairground depends to a great extent on mathematics. Mathematics is used in the design of rides, such as a rollercoaster or a Ferris wheel, and in impressive shows, such as a choreographed water show or fireworks.

 

In this lesson you will continue to investigate linear-quadratic and quadratic-quadratic systems. You will learn how to solve these types of systems algebraically. You will use methods that are similar to those that you have previously studied.

 

Outcomes

 

At the end of this lesson you will be able to

• determine and verify the solution of a system of linear-quadratic or quadratic-quadratic equations algebraically
  
  
• solve a problem that involves a system of linear-quadratic or quadratic-quadratic equations and explain the strategy used
  
  
• model a situation using a system of linear-quadratic or quadratic-quadratic equations

Lesson Questions

 

You will investigate the following questions:

• Why do systems of equations yield the correct solutions even after they have been manipulated algebraically?
  
  
• Why is it important to be able to solve systems of equations algebraically as well as graphically?

Assessment

Your assessment may be based on a combination of the following tasks:

• completion of the Lesson 6 Assignment (Download the Lesson 6 Assignment and save it in your course folder now.)
  
  
• course folder submissions from Try This and Share activities
  
  
• additions to Module 4 Glossary Terms and Formula Sheet
  
  
• work under Project Connection