Topicmbf27f9072bd8b839_1528449000663_0Topic

A system of linear equationssystem of linear equationssystem of linear equations

Levelmbf27f9072bd8b839_1528449084556_0Level

Third

Core curriculummbf27f9072bd8b839_1528449076687_0Core curriculum

IV. Systems of equations. The student:

1) solves systems of linear equations with two unknowns, gives geometric interpretation of consistent dependent and independent systems as well as inconsistent systems.

Timingmbf27f9072bd8b839_1528449068082_0Timing

45 minutes

General objectivembf27f9072bd8b839_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesmbf27f9072bd8b839_1528449552113_0Specific objectives

1. Solving systems of equations.

2. Communicating in English, developing basic mathematical, computer and scientific competences, developing learning skills.

Learning outcomesmbf27f9072bd8b839_1528450430307_0Learning outcomes

The student:

- solves systems of equations.

Methodsmbf27f9072bd8b839_1528449534267_0Methods

1. Discussion.

2. Task tables.

Forms of workmbf27f9072bd8b839_1528449514617_0Forms of work

1. Work in pairs.

2. Group work.

Lesson stages

Introductionmbf27f9072bd8b839_1528450127855_0Introduction

The teacher introduces the subject of the lesson - revising ways of solving systems of equations and learning types of equations.

Procedurembf27f9072bd8b839_1528446435040_0Procedure

Task
Students do the task using the elimination methodelimination methodelimination method and compare their solutions to the one in the multimedia illustration.

[Interactive illustration]

Students’ conclusion:

- A pair of numbers satisfies the given system of first degree equations with two unknown if it satisfies both equations of this system. Students work in groups using the task tables method.

Task - Table 1
We call a system of equations inconsistent if it has zero solutions. Insert such number in the dotted space that the system is inconsistent.

Task - Table 2
A system od equation is consistent independent if it has exactly one solution.
A system of equation is consistent dependent if it has infinitely many solutions.
By solving the system using the substitution method we obtain an equation
5x – 4 = 5x + 1. Does it mean this system is consistent independent, consistent dependent or inconsistent?mbf27f9072bd8b839_1527752263647_0A system od equation is consistent independent if it has exactly one solution.
A system of equation is consistent dependent if it has infinitely many solutions.
By solving the system using the substitution method we obtain an equation
5x – 4 = 5x + 1. Does it mean this system is consistent independent, consistent dependent or inconsistent?

Task - Table 3
Solve this system of equations using any method.mbf27f9072bd8b839_1527752256679_0Solve this system of equations using any method.

Task - Table 4
Find all real numbers m for which the system of equations has no solutions.

An extra task:
Write a system of equations with two unknown whose solution is the pair of numbers. (-1, 4).mbf27f9072bd8b839_1527712094602_0An extra task:
Write a system of equations with two unknown whose solution is the pair of numbers. (-1, 4).

Groups present results of their work. The teacher clarifies doubts and evaluates groups’ work.

Lesson summarymbf27f9072bd8b839_1528450119332_0Lesson summary

Students do the revision exercises.

Then together they sum‑up the classes, by formulating the conclusions to memorise.

- A pair of numbers satisfies the given system of first degree equations with two unknown if it satisfies both equations of this system.

Selected words and expressions used in the lesson plan

consistent dependent systemconsistent dependent systemconsistent dependent system

consistent independent systemconsistent independent systemconsistent independent system

elimination methodelimination methodelimination method

inconsistent systeminconsistent systeminconsistent system

substitution methodsubstitution methodsubstitution method

system of linear equationssystem of linear equationssystem of linear equations