Lesson 4: Solving Linear Systems by Elimination: Explore 2

Module 7: Systems of Linear Equations

Read

You have seen how to use multiplication and subtraction to solve a linear system. Go to your textbook now to study examples of how elimination by addition can be used to solve linear systems. As you study the solutions, try to find the answers to the following questions:

How do you prepare a linear system for elimination by addition?
How is this different from preparing for elimination by subtraction?

Foundations and Pre-calculus Mathematics 10 (Pearson)
Read “Example 2: Solving a Linear System by Adding to Eliminate a Variable” on pages 432 and 433.

Watch and Listen

Go and watch the webcast Solving Systems using Elimination. You can also check out the other resources on this page as well.

Try This 4

Complete the following in your binder.
Foundations and Pre-calculus Mathematics 10 (Pearson)
TT 4. Complete “Exercises” questions 3, 6, and 12 on pages 437 and 438.
Use the link below to check your answers to Try This 4.
Possible TT4 Solutions

Read

You can use the elimination method to solve problems modelled by systems of linear equations. Go to your textbook to see how a problem is modelled and then solved by elimination. As you read, pay attention to the following:
->How is the information from the problem organized?
->How are the equations of the model prepared for the elimination of a variable?

Foundations and Pre-calculus Mathematics 10 (Pearson)

Read “Example 3: Using a Linear System to Solve a Problem” on page 434.

Try This 5

Study each of the following problems. In Lesson 3 you chose one of the problems to model with a linear system. You will now use a system of equations to model the other problem. If you chose Problem 1 in Lesson 3, choose Problem 2 to answer TT 5 and vice-versa.
TT 5. Define the variables and solve the system using the method of elimination. Include any tables or diagrams that you may have used to help with the setup of the system.
Problem 1: The admission fee for the chuck wagon races at the Grande Prairie Stampede is $10.00 for children and $16.00 for adults. On a certain day, 2200 people enter the fair and $30 544 is collected. Determine the number of children and the number of adults that attended on this day.
OR
Problem 2: An exam worth 125 points contains 40 questions. Some of the questions are worth two points and some are worth five points. Determine the number of two-point questions and the number of five-point questions.
Possible TT5 Solutions