Mathematics 10C Module 7 Lesson 5

Module 7: Systems of Linear Equations

 What happens if you try to algebraically solve a linear system that has either no solutions or an infinite number of solutions? What will your answer look like? To find out, complete the Try This questions below.

Try This 13 - 16

 

Complete the following.
Try This 13 - 16 Questions
Use the link below to check your answers to Try This 13 - 16.
Possible TT13-16 Solutions

Read

Go to your textbook to solidify your understanding of how the number of solutions of a linear system relate to the terms of the equations in the system.

Foundations and Pre-calculus Mathematics 10 (Pearson)

 

Read “Example 2: Creating a Linear System with 0, 1, or Infinite Solutions” on page 446. As you read, focus on the differences between the methods used in parts a) and b) compared to part c).



Self-Check

SC 4.

  1. In the system of linear equations y = 2x + 3 and y = 2x + b, what values of b will result in a system that has no solution?
  2. What values of b will result in a system that has one solution?
  3. What values of b will result in a system that has an infinite number of solutions?

SC 5.

  1. In the system of linear equations y = -3x + 4 and y = mx + 4, what values of m will result in a system that has no solution?
  2. What values of m will result in a system that has one solution?
  3. What values of m will result in a system that has an infinite number of solutions?

SC 6. How many solutions does each linear system have? Show how you know.

  1. 2x + 3y = 20
    6x - y = 20
  2. x - 5y = 1
    -x + 5y = 1
  3. x + 3y = 5
    2x + 6y = 10

To help you with SC 7, retrieve your flow chart from Try This 12. You created it for identifying the number of solutions in a linear system. Think about the strategies that you used and that can be applied to this problem. Do the question; then return to the flow chart to evaluate its success in tackling this problem. Make any necessary revisions to the flow chart.

SC 7. Consider the following four linear equations.

Line

Considerations

A

6x + 2y = 16

B

9x + 3y = 12

C

-3x + y = 8

D

6x - 2y = -16
  1. Identify two lines that form a system that has no solution.
  2. Identify two lines that form a system that has one solution.
  3. Identify two lines that form a system that has an infinite number of solutions.

Compare your answers.

Try This 17

 

For some final practice, complete the following in your binder.

Foundations and Pre-calculus Mathematics 10 (Pearson)

TT 17. Complete “Exercises” questions 4, 5, 6, 7, 10, 11, and 12 on page 448.
Use the link below to check your answers to Try This 17.
Possible TT17 Solutions

---------------------------------

Now it's time to have some fun playing a game to practice all of the skills you have learned about Linear Systems.

Use the link below to play the Flying Acrobats game.

---------------------------------