Simultaneous Linear Equations (II)

Grade 9 · Mathematics

Semester 1 | Period 3 | Week 15

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Subject: Mathematics

Semester: 1

Period: 3

Week: 15

WEEK 15

Class: Grade 9
Age: 14 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Simultaneous Linear Equations (II)
Focus: Graphical Method & Compilation of Table of Values

Specific Objectives:

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

  1. Construct a table of values for linear equations in two variables.
  2. Plot straight-line graphs from equations using the table of values.
  3. Solve simultaneous linear equations graphically.
  4. Interpret the solution of simultaneous equations from the point of intersection.
  5. Relate the graphical method to real-life applications.

 

Instructional Techniques:

  • Question and answer
  • Guided demonstration
  • Group practice
  • Graph plotting and illustration
  • Problem-solving drills

 

Instructional Materials:

  • Graph paper
  • Rulers and pencils
  • Whiteboard and marker
  • Flashcards with linear equations
  • Calculator (optional)

 

PERIOD 1 & 2: Compilation of Table of Values for Linear Equations

Presentation:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 – Introduction

Explains that every straight-line equation can be represented by a set of values for x and y.

Pupils listen and ask questions.

Step 2 – Explanation

Demonstrates how to substitute values of x into y=2x+1 to build a table of values.

Pupils observe and practice.

Step 3 – Guided Practice

Guides pupils in completing tables for other linear equations.

Pupils calculate values in groups.

Step 4 – Note Taking

Writes procedures and examples on the board.

Pupils copy notes into their books.

 

Note on Board:

  • A table of values helps to generate coordinate points for plotting.
  • Example: For y=2x+1:

x

-2

-1

0

1

2

y

-3

-1

1

3

5

 

Evaluation (5 exercises):

  1. Complete a table of values for y=x+2 when x=−2,−1,0,1,2
  2. Construct a table for y=3 x−1.
  3. Generate values for y=−x+4.
  4. Form a table for 2x+y=6.
  5. Generate points for x−y=1.

 

Classwork (5 questions):

  1. Complete the table for y=2x−3.
  2. Generate points for y=−2x+5.
  3. Form a table for 3x+y=9.
  4. Construct a table for x+y=7.
  5. Generate points for 2x−y=4.

 

Assignment (5 tasks):

  1. Construct a table of values for y = 4x + 1.
  2. Complete the table for y=−3x+2.
  3. Generate values for y=1/2x+3.
  4. Form a table for 3x−2y=6.
  5. Prepare a table of values for x+2y=8.

 

PERIOD 3 & 4: Solving Simultaneous Equations Using the Graphical Method

Presentation:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 – Introduction

Explains how two linear equations can be solved by plotting both on the same graph.

Pupils listen attentively.

Step 2 – Explanation

Demonstrates with 2x + y = 6 and x - y = 1, creating tables and plotting graphs.

Pupils practice plotting.

Step 3 – Guided Practice

Provides more pairs of equations for pupils to solve graphically.

Pupils work in groups using graph paper.

Step 4 – Note Taking

Writes steps on solving simultaneous equations graphically.

Pupils copy into their notes.

 

Note on Board:

Steps to Solve Simultaneous Equations Graphically:

  1. Convert each equation into the form y=mx+c.
  2. Construct a table of values for each equation.
  3. Plot both equations on the same graph.
  4. The point where the two lines intersect is the solution.

 

Evaluation (5 exercises):

  1. Solve graphically: 2x+y=6 and x - y = 1.
  2. Solve: x + y = 5 and x−y=3.
  3. Find the solution of: 3x−y=4 and x+y=6.
  4. Solve: 2x+3y=12 and x−y=2.
  5. Graph: x+2y=8 and 3x−y=9.

Classwork (5 questions):

  1. Plot and solve: x + y = 7, 2x - y = 3.
  2. Solve graphically: 2x−y=5, x+y=4.
  3. Graph and solve: y = 2x + 1, y=−x+4.
  4. Solve: 3x+2y=12, x - y = 2.
  5. Solve graphically: 4x−y=8, x + y = 6.

 

Assignment (5 tasks):

  1. Solve graphically: 2x+y=7, x−y=2.
  2. Plot and solve: y = x + 2, y=−2x+6.
  3. Graph and solve: 3x−2y=4, x+y=5.
  4. Solve: 2x+3y=9, x−y=1.
  5. Write a real-life word problem that can be solved using simultaneous equations, then represent it graphically.

 

PERIOD 5: Interpretation of Graphical Solutions

Presentation:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 – Introduction

Explains how the intersection point represents the solution.

Pupils listen.

Step 2 – Explanation

Shows practical problems (e.g., comparing prices, budgeting).

Pupils observe.

Step 3 – Guided Practice

Gives more examples of real-life applications.

Pupils practice.

Step 4 – Independent Practice

Pupils solve similar problems on their own.

Pupils work independently.

 

Note on Board:

  • The intersection point (x, y) is the solution to both equations.
  • Real-life uses: business profits, resource distribution, budgeting.

 

Evaluation (3 problems):

  1. A pen and a pencil cost 100dollars together. A pen costs 20dollars more than a pencil. Represent and solve this problem graphically.
  2. A rectangle’s length is 3 times its width. The perimeter is 48 cm. Represent as equations and solve graphically.
  3. Two numbers add to 12. Their difference is 4. Solve graphically.