Topicmea1f4f5a04fb36a0_1528449000663_0Topic

The substitution methodsubstitution methodsubstitution method of solving system of equations – improving skills

Levelmea1f4f5a04fb36a0_1528449084556_0Level

Third

Core curriculummea1f4f5a04fb36a0_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.

Timingmea1f4f5a04fb36a0_1528449068082_0Timing

45 minutes

General objectivemea1f4f5a04fb36a0_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesmea1f4f5a04fb36a0_1528449552113_0Specific objectives

1. Improving skills related to solving system of equations using the substitution method.

2. Applying systems of equations to solve simple mathematical problems.

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

Learning outcomesmea1f4f5a04fb36a0_1528450430307_0Learning outcomes

The student:

- improves skills related to solving system of equations using the substitution method,

- applies systems of equations to solve simple mathematical problems.

Methodsmea1f4f5a04fb36a0_1528449534267_0Methods

1. Situational analysis.

2. Task contest.

Forms of workmea1f4f5a04fb36a0_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmea1f4f5a04fb36a0_1528450127855_0Introduction

Students revise the learnt method of solving systems of equations – the substitutionsubstitutionsubstitution method.

Proceduremea1f4f5a04fb36a0_1528446435040_0Procedure

Students work individually, using computers. Their task is to know the interactive illustration, that helps them revise the method of solving systems of equations they learnt during the previous lesson.

[Interactive graphics] 

After having completed the exercise, they write down conclusions:

While solving the system of equations using the substitution methodsubstitution methodsubstitution method, we follow these steps:

1. We isolate x from the first equation
2. We substitute the obtained expression for the x in the second equation.
3. After the substitution, the second equation becomes an equation with one unknown y – we solve it. We rewrite the first equation in the same form.
4. After calculating the value of y, we substitute it to the first equation and by making proper operations, we calculate the value of x.
5. The pair of numbers that is the solution of the system of equations.mea1f4f5a04fb36a0_1527752263647_01. We isolate x from the first equation
2. We substitute the obtained expression for the x in the second equation.
3. After the substitution, the second equation becomes an equation with one unknown y – we solve it. We rewrite the first equation in the same form.
4. After calculating the value of y, we substitute it to the first equation and by making proper operations, we calculate the value of x.
5. The pair of numbers that is the solution of the system of equations.

The teacher gives out worksheets with systems of equations (the level of difficulty of tasks varies from easy to difficulty).

Students take part in the individual task contest by doing exercises from 4 levels of difficulty.

Three students with the highest number of points get the highest grades, three consecutive – second highest grades.

Task 1

Solve systems of equations using the substitution method.

Level 1 – each correct answer is worth 1 point.

- $\left\{\begin{array}{l}x=3\\ 2x+y=8\end{array}\right.$
- $\left\{\begin{array}{l}3x-y=5\\ -y=2\end{array}\right.$
- $\left\{\begin{array}{l}x+y=3\\ x-y=1\end{array}\right.$

Level 2 – each correct answer is worth 2 points.

- $\left\{\begin{array}{l}2x-y=3\\ x+y=12\end{array}\right.$
- $\left\{\begin{array}{l}5x+2y=15\\ 2x-y=4\end{array}\right.$

Level 3 – each correct answer is worth 3 points.

- $\left\{\begin{array}{l}5(x-2y)=12y\\ 3x+2(y-x)=10\end{array}\right.$

Level 4 – each correct answer is worth 4 points.

- $\left\{\begin{array}{l}\frac{2x+y}{2}-\frac{x-y}{3}=\frac{2x}{5}\\ \frac{x-2(y-x)}{4}=\frac{1}{2}\end{array}\right.$

The teacher evaluates students’ work and clarifies doubts.

An extra task
For what m number this system of equations has no solutions?

Lesson summarymea1f4f5a04fb36a0_1528450119332_0Lesson summary

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

While solving the system of equations using the substitution method, we follow these steps:

1. We isolate x from the first equation
2. We substitute the obtained expression for the x in the second equation.
3. After the substitution, the second equation becomes an equation with one unknown y – we solve it. We rewrite the first equation in the same form.
4. After calculating the value of y, we substitute it to the first equation and by making proper operations, we calculate the value of x.
5. The pair of numbers that is the solution of the system of equations.mea1f4f5a04fb36a0_1527752263647_01. We isolate x from the first equation
2. We substitute the obtained expression for the x in the second equation.
3. After the substitution, the second equation becomes an equation with one unknown y – we solve it. We rewrite the first equation in the same form.
4. After calculating the value of y, we substitute it to the first equation and by making proper operations, we calculate the value of x.
5. The pair of numbers that is the solution of the system of equations.

Selected words and expressions used in the lesson plan

first degree system of equationsfirst degree system of equationsfirst degree system of equations

isolating the variableisolating the variableisolating the variable

ordered pair of numbersordered pair of numbersordered pair of numbers

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

substitutionsubstitutionsubstitution

substitution methodsubstitution methodsubstitution method

transforming the equationtransforming the equationtransforming the equation