Mathematics - Junior Secondary 3 - Simultaneous Linear Equations (I) – In One or Two Variables Using Elimination and Subtraction Methods

Simultaneous Linear Equations (I) – In One or Two Variables Using Elimination and Subtraction Methods

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TERM: 2ND TERM

WEEK 1
Class: Junior Secondary School 3
Age: 14 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Simultaneous Linear Equations (I) – In One or Two Variables Using Elimination and Subtraction Methods
Focus: Elimination and Subtraction Methods

SPECIFIC OBJECTIVES:
By the end of the lesson, pupils should be able to:

  1. Solve simultaneous linear equations using the elimination method.
  2. Solve simultaneous linear equations using the subtraction method.
  3. Understand the concept of equations with one or two variables.
  4. Identify the relationship between different variables in simultaneous equations.
  5. Apply the methods to solve word problems.

INSTRUCTIONAL TECHNIQUES:
• Question and answer
• Guided demonstration
• Class discussion
• Group work
• Real-life application

INSTRUCTIONAL MATERIALS:
• Whiteboard and markers
• Graph paper
• Worksheets with problems
• Calculator (optional)

PERIOD 1 & 2: Introduction to Simultaneous Equations and Elimination Method
PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Introduces the concept of simultaneous equations. Explains that they can be solved using different methods.

Pupils listen and ask questions.

Step 2 - Explanation

Defines simultaneous equations and introduces the elimination method. Presents an example: 2x + 3y = 10 and 4x + 6y = 20.

Pupils follow along and take notes.

Step 3 - Demonstration

Solves the given example using the elimination method: multiply both equations by suitable values to eliminate one variable.

Pupils watch, observe, and ask questions.

Step 4 - Practice

Provides practice problems for pupils to solve in pairs using the elimination method.

Pupils work in pairs, solving the problems.

Step 5 - Note-Taking

Teacher writes down the general steps for the elimination method on the board.

Pupils take notes.

NOTE ON BOARD:

  • Elimination Method:
  1. Multiply or divide equations by a number to align the coefficients of one variable.
  2. Add or subtract the equations to eliminate one variable.
  3. Solve for the remaining variable.
  4. Substitute the value of the solved variable into one of the original equations to find the other variable.

EVALUATION (5 exercises):

  1. Solve: 2x + 3y = 12 and 4x + 5y = 20
  2. Solve: 3x – 2y = 6 and 5x + 3y = 15
  3. Solve: 4x + 2y = 10 and 3x – 5y = 7
  4. Solve: 5x + 4y = 12 and 3x + 6y = 18
  5. Solve: 6x – 7y = 15 and 2x + 3y = 8

CLASSWORK (5 questions):

  1. Solve: 2x + y = 10 and 3x + 2y = 14
  2. Solve: 4x – y = 5 and 6x + y = 9
  3. Solve: 5x + 3y = 11 and 2x + 4y = 8
  4. Solve: 3x – 2y = 7 and 6x + y = 13
  5. Solve: 2x + 5y = 9 and 4x + 3y = 12

ASSIGNMENT (5 tasks):

  1. Solve: 3x + 5y = 12 and 2x – 3y = 7
  2. Solve: 4x + 6y = 24 and 2x + 5y = 20
  3. Solve: 7x – 4y = 10 and 6x + 3y = 12
  4. Solve: 5x + 3y = 15 and 7x + 4y = 20
  5. Solve: 8x – 2y = 16 and 5x + y = 14

 

PERIOD 3 & 4: Subtraction Method
PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Introduces the subtraction method. Explains that it involves subtracting one equation from another to eliminate a variable.

Pupils listen and ask questions.

Step 2 - Explanation

Presents an example: 3x + 2y = 15 and 5x + 3y = 20. Shows how to multiply the equations to align the coefficients for subtraction.

Pupils observe and take notes.

Step 3 - Demonstration

Solves the example by subtracting the equations to eliminate one variable.

Pupils follow along and practice on their own.

Step 4 - Practice

Provides practice problems for pupils to solve in pairs using the subtraction method.

Pupils work in pairs to solve problems.

Step 5 - Note-Taking

Teacher writes down the general steps for the subtraction method on the board.

Pupils take notes.

NOTE ON BOARD:

  • Subtraction Method:
  1. Multiply the equations to align the coefficients of one variable.
  2. Subtract one equation from the other to eliminate one variable.
  3. Solve for the remaining variable.
  4. Substitute the value of the solved variable into one of the original equations to find the other variable.

EVALUATION (5 exercises):

  1. Solve: 3x + 4y = 18 and 5x + 6y = 26
  2. Solve: 4x + 5y = 20 and 2x + 3y = 12
  3. Solve: 7x + 3y = 19 and 5x + 2y = 14
  4. Solve: 6x + 4y = 16 and 2x + 5y = 14
  5. Solve: 8x + 3y = 24 and 4x + 2y = 12

CLASSWORK (5 questions):

  1. Solve: 2x + y = 5 and 3x + 2y = 9
  2. Solve: 3x – 2y = 10 and 4x + 3y = 15
  3. Solve: 6x + 2y = 18 and 3x + 4y = 16
  4. Solve: 5x + 3y = 12 and 7x + 2y = 15
  5. Solve: 4x – 3y = 8 and 3x + 2y = 7

ASSIGNMENT (5 tasks):

  1. Solve: 6x + y = 14 and 3x + 4y = 10
  2. Solve: 3x – 2y = 6 and 5x + 3y = 13
  3. Solve: 2x + 3y = 10 and 4x – y = 8
  4. Solve: 7x + 2y = 17 and 5x + 3y = 12
  5. Solve: 3x + 4y = 18 and 2x – 5y = 7

 

PERIOD 5: Application of Simultaneous Equations (Elimination and Subtraction Methods)
PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Introduces real-life problems involving simultaneous equations. Explains how to apply elimination and subtraction methods to solve them.

Pupils listen and ask questions.

Step 2 - Examples

Presents examples involving word problems like distances, mixtures, and financial calculations.

Pupils solve the problems with guidance.

Step 3 - Drill

Provides word problems for pupils to solve using both methods.

Pupils write solutions and discuss them.

Step 4 - Evaluation

Reviews the answers with the class and discusses common mistakes.

Pupils discuss their solutions and understand mistakes.

EVALUATION (5 questions):

  1. If 2x + y = 10 and 3x + 4y = 20, solve for x and y.
  2. A car travels 40 miles per hour for 3 hours, and another car travels 50 miles per hour for 2 hours. How far did each car travel?
  3. A grocer mixes two types of flour, one costing $5 per kg and the other costing $8 per kg. If the mixture weighs 10 kg and costs $7 per kg, how many kg of each type did he use?
  4. Solve: 4x – y = 6 and 3x + 2y = 10
  5. Solve: 5x + 2y = 15 and 3x + 4y = 17

CLASSWORK (5 tasks):

  1. Solve: 3x + y = 12 and 2x + 3y = 10
  2. A person buys 3 apples for $1.50 and 5 bananas for $2. Find the cost of 1 apple and 1 banana.
  3. Solve: 4x + y = 8 and 3x + 2y = 10
  4. A tank is filled with two pipes, one filling at 10 liters per minute and the other at 15 liters per minute. If the tank is filled in 4 minutes, how many minutes would it take for each pipe

to fill the tank alone?
5. Solve: 3x + 4y = 14 and 2x + 3y = 10

ASSIGNMENT:

  1. Solve: 5x + 3y = 12 and 3x + 4y = 10
  2. A factory produces 200 units of product A and 300 units of product B. If product A costs $10 per unit and product B costs $12 per unit, how much does the factory earn from both products?
  3. Solve: 7x + 2y = 20 and 4x + 3y = 18
  4. A plane travels 200 miles in 2 hours with wind and 180 miles in 2 hours against the wind. What is the speed of the plane and the speed of the wind?

Solve: 6x + y = 10 and 3x + 2y = 12