Simultaneous Linear Equations (III)

Grade 9 · Mathematics

Semester 1 | Period 3 | Week 16

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Subject: Mathematics

Semester: 1

Period: 3

Week: 16

WEEK 16
Class: Grade 9
Age: 14 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Simultaneous Linear Equations (III)
Focus: More Exercises on Simultaneous Linear Equations using Graphical Method
Specific Objectives:
By the end of the lesson, pupils should be able to:

  1. Solve simultaneous linear equations using the graphical method.
  2. Interpret the solution of the equations graphically.
  3. Apply the graphical method to real-life problems.
  4. Draw and interpret graphs of linear equations.
  5. Solve word problems involving simultaneous linear equations.

Instructional Techniques:
• Question and answer
• Guided demonstration
• Problem-solving activities
• Graphical illustration
• Drills and exercises

Instructional Materials:
• Graph paper
• Rulers and pencils
• Whiteboard and marker
• Flashcards with problems
• Calculator (optional)

PERIOD 1 & 2: More Exercises on Simultaneous Linear Equations using Graphical Method

Presentation:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Explains the graphical method of solving simultaneous linear equations. Shows how to plot lines and find the intersection.

Pupils observe and ask questions.

Step 2 - Explanation

Demonstrates solving an example using the graphical method on the whiteboard.

Pupils practice plotting the graphs on paper.

Step 3 - Guided Practice

Solves more problems with the class, involving plotting the lines and finding the intersection.

Pupils work through problems with guidance.

Step 4 - Note Taking

Teacher writes the steps of solving linear equations graphically.

Pupils copy down the procedure.

Note on Board:

  • To solve using the graphical method:
  1. Plot each linear equation as a straight line.
  2. Identify the point where both lines intersect.
  3. The coordinates of the intersection point give the solution to the equations.

Evaluation (5 exercises):

  1. Solve: 2x + y = 6 and x – y = 1 using the graphical method.
  2. Solve: 3x – 2y = 4 and x + y = 5.
  3. Solve: 4x – 3y = 12 and x + 2y = 6.
  4. Plot the equations: x + y = 7 and 2x – y = 4.
  5. Find the solution to the system of equations using graphs: x + 2y = 8 and 3x – y = 10.

Classwork (5 questions):

  1. Plot the lines for the system of equations: 5x + 2y = 15 and x – y = 2.
  2. Solve: x + 3y = 7 and 2x – y = 5 using the graphical method.
  3. Graph the equations: 2x – y = 6 and x + y = 4.
  4. Solve the system using graphs: x + 2y = 10 and 2x – y = 8.
  5. Find the intersection point of the following equations: 3x – 4y = 5 and x + y = 6.

Assignment (5 tasks):

  1. Solve: x – y = 3 and 2x + y = 9 using the graphical method.
  2. Draw the graphs for: 3x + y = 7 and x + 3y = 5.
  3. Solve the equations using graphs: 5x – 3y = 10 and x + 2y = 8.
  4. Plot and solve: 2x + 3y = 12 and x – 2y = 1.
  5. Write a word problem that can be solved using simultaneous equations and solve it graphically.

 

PERIOD 3 & 4: Application of Simultaneous Linear Equations to Life Situations using Problem Solving

Presentation:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Introduces real-life applications of simultaneous linear equations (e.g., finance, distance problems, mixtures).

Pupils listen and ask questions.

Step 2 - Explanation

Solves real-life problems involving simultaneous linear equations (e.g., two companies sharing a contract, a school distributing resources).

Pupils work with the teacher on real-life problems.

Step 3 - Guided Practice

Solves additional real-life examples step-by-step.

Pupils practice solving real-life word problems.

Step 4 - Independent Practice

Pupils work on similar word problems individually.

Pupils solve problems on their own.

Note on Board:

  • Real-life examples can be solved using simultaneous linear equations:
  1. Example: A company produces 200 units of product A and 300 units of product B. If product A costs $10 and product B costs $12, how much revenue does the company earn?
  2. Example: If two trains are 100 miles apart and they start at the same time heading towards each other, how long will it take them to meet?

Evaluation (5 exercises):

  1. A gardener plants 100 trees in two rows. The number of trees in the first row is 20 more than the number of trees in the second row. How many trees are in each row?
  2. Solve: Two numbers add up to 80, and their difference is 12. Find the numbers.
  3. Two workers are paid $120 and $150 respectively for their work. If the total payment is $270, how much did each worker contribute?
  4. A school has 300 students in total. There are 120 more girls than boys. How many boys and girls are there?
  5. A family spends $3000 on food, entertainment, and transportation. If the entertainment budget is $500 more than the transportation budget, and the food budget is $100 more than the transportation budget, how much did they spend on each?

Classwork (5 tasks):

  1. Solve: The sum of two numbers is 100, and their difference is 30. What are the numbers?
  2. A company produces pens and pencils. The total number of pens and pencils produced is 500. If the number of pens is 200 more than the number of pencils, how many pens and pencils are produced?
  3. Two bicycles and a pair of shoes cost $3000. The bicycles cost $1000 more than the shoes. How much does each cost?
  4. A movie theater sold 100 tickets for a concert. The total revenue was $5000. If tickets for adults cost $50 and tickets for children cost $30, how many adult and child tickets were sold?
  5. A car rental company charges a $50 rental fee per day and $10 per mile. A customer rents a car for 3 days and drives 150 miles. What is the total charge?

Assignment (5 tasks):

  1. A family has a combined income of $5000 per month. The husband earns $1000 more than the wife. How much does each earn?
  2. A school has 200 students. The number of boys is 50 more than twice the number of girls. How many boys and girls are there?
  3. Solve the problem: The sum of two numbers is 50, and their difference is 10. What are the numbers?
  4. A bank charges $10 monthly for an account and $2 per transaction. If a customer’s monthly fee is $40, how many transactions did they make?
  5. A company produces 500 units of two products, X and Y. If the number of X is 100 more than double the number of Y, how many units of each product were produced?