Lesson 5: Number of Solutions of a Linear System

Module 7: Systems of Linear Equations

Lesson 5: Number of Solutions of a Linear System

Focus

 

Have you ever watched an ensemble dance performance? Perhaps you’ve attended a musical production or tuned in to a television program featuring competitive dancing. If you have, then you might have been impressed with the way that the dancers’ movements were synchronized, both with the music and with each other. The art of designing sequences of movement to form a dance is called choreography.

In addition to dance, choreography is used in other contexts that involve movement. Moves and routines are developed or choreographed in activities such as cheer leading, gymnastics, figure skating, fashion shows, and combat scenes, including sword fights in stage productions. In cheer leading, for example, you may also see pyramid formations. In ensemble choreography, you will often see different formations of the performers, including straight lines, rows, crosses, and staggered V-formations.

In this lesson you will investigate the formations of two lines. From Lesson 1 you are already familiar with the fact that two lines can intersect at a single point. In this lesson you will study the relative orientations of two lines on a coordinate plane and determine the implications for the number of solutions of such linear systems.

Outcome

At the end of this lesson, you will be able to explain, using examples, why a system of equations may have no solution, one solution, or an infinite number of solutions.

Lesson Questions

• Why can linear systems have different numbers of solutions?
• How do the equations of a linear system indicate the number of solutions of that system?

Lesson Assessment and Completion

 

As you work through each lesson, complete all the questions and learning activities in your binder using paper and pencil, clearly labeling your work (they refer to this as your course folder). These include the Are you Ready, Try This, Share and Self Check questions. Check your work if answers are provided. Remember that these questions provide you with the practice and feedback that you need to successfully complete this course.
Once you have completed all of the learning activities, take the Lesson Quiz. This is the assessment for each lesson and is located under the Activities block on the left in moodle or under the Assess tab.

** Note – Share questions may have to be done on your own depending on your learning situation**

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