Topicm3013559132634c82_1528449000663_0Topic

Solving systems of equations using the method of elimination

Levelm3013559132634c82_1528449084556_0Level

Third

Core curriculumm3013559132634c82_1528449076687_0Core curriculum

IV Systems of equations. Student:

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

Timingm3013559132634c82_1528449068082_0Timing

45 minutes

General objectivem3013559132634c82_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm3013559132634c82_1528449552113_0Specific objectives

1. Solving systems of equations using the method of elimination.

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

Learning outcomesm3013559132634c82_1528450430307_0Learning outcomes

Student:

- Solves systems of equations using the method of elimination.

Methodsm3013559132634c82_1528449534267_0Methods

1. Discussion.

2. For and against debate.

Forms of workm3013559132634c82_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm3013559132634c82_1528450127855_0Introduction

A students chosen by the teacher revises information about systems of equations. This student lists types of systems of solutions with regard to the number of solutions and gives appropriate examples.

The teacher introduces the subject of the lesson – solving systems of equations using the elimination methodelimination methodelimination method.

A few days before the lesson, the teacher asks two students to prepare a for and against debate and to moderate the discussion. Those students prepare a few examples describing the solution of systems of equations using the elimination methodelimination methodelimination method.

Procedurem3013559132634c82_1528446435040_0Procedure

[Slideshow]

Students work individually, using computers. Their task is to observe the solution of a task using the elimination methodelimination methodelimination method.

For and against debate

The teacher introduces the subject of the debate and sets the rules. The debate is supposed to analyse exemplary solutions of system of equations. Moderators (experts) present examples they prepared. They start a discussion 0 is such method of solving the system of equations effective, easy for students, increases the risk of making mistakes or maybe decreases it, etc.

Moderators give or take a chance to speak, cut statements that are too long or off topic. The discussion about one example should last about 4 minutes, then they move on to the next example. The observants decide whose arguments are more convincing.

Students’ conslusions

The elimination method of solving systems of equations is adding or subtracting sides of the equation to eliminate one of the unknowns and to obtain a first degree equation with one unknown. m3013559132634c82_1527752263647_0The elimination method of solving systems of equations is adding or subtracting sides of the equation to eliminate one of the unknowns and to obtain a first degree equation with one unknown. 

Task 1
Solve the system of equations using the substitution method and the elimination methodelimination methodelimination method.

a. $\left\{\begin{array}{l}x+y=3\\ x-2y=-1\end{array}\right.$

b. $\left\{\begin{array}{l}4x+y=2\\ x-2y=3\end{array}\right.$

c. $\left\{\begin{array}{l}x+2y=-4\\ x-2y=0\end{array}\right.$

Task 2
Janek and Maciek collect bookmarks. Together they have 57 of them. If Janek gives Maciek 7 bookmarks then both of them will have the same amount of bookmarks. Calculate how many bookmarks each boy has. Write a proper system of equations and solve it using the elimination methodelimination methodelimination method.

Task 3
What kind of system of equations will we obtain, if while solving the system using the elimination methodelimination methodelimination method we obtain an equation in the form of:
-4x - 4x – 2 = -2?

Task 4
Solve systems of equations using the elimination methodelimination methodelimination method.

a. $\left\{\begin{array}{l}2x+y=2\\ 5x-3y=-1\end{array}\right.$

b. $\left\{\begin{array}{l}7x+2y=4\\ 2x+5y=2\end{array}\right.$

c. $\left\{\begin{array}{l}2x+5y=-2\\ 3x-2y=5\end{array}\right.$

An extra task:

Stanisław bought two shirts and shorts. Shorts cost 150 zł. Ignacy bought the same clothes on sale He paid 20% less for the shirt and 10% less for shorts and together he spent 127 zł. How much did the shirt and shorts cost before the sale? Write a proper system of equations and solve it using the elimination method.

Lesson summarym3013559132634c82_1528450119332_0Lesson summary

Students do the revision exercises. Then together they sum‑up the classes, by formulating the conclusions to memorise.

The elimination methodelimination methodelimination method of solving systems of equations is adding or subtracting sides of the equation to eliminate one of the unknowns and to obtain a first degree equation with one unknown.

Selected words and expressions used in the lesson plan

elimination methodelimination methodelimination method

solution of the system of equationssolution of the system of equationssolution of the system of equations

subtraction methodsubtraction methodsubtraction method

system of first degree equations with two unknownssystem of first degree equations with two unknownssystem of first degree equations with two unknowns