Class: Junior Secondary School 3 (JSS3, JSS 3)
Term: 1st Term
Week: 9
Age: 14 years
Duration: 45 minutes
Subject: Mathematics
Curriculum Theme: Mathematics
Previous Lesson: Solving Simultaneous Equations by Substitution and Elimination Methods
Topic: Graphical Solution of Simultaneous Equations
Subject Matter: Compiling table of values for simultaneous linear equations, Solving problems involving simultaneous linear equations in 2 variables graphically.

Specific Objectives

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

Cognitive Domain:
(a) Construct a table of values for given linear equations in two variables.
(b) Solve simultaneous equations graphically by plotting two linear equations on the same axes and identifying the point of intersection.
Affective Domain:
(a) Develop interest and confidence in solving simultaneous equations using graphical methods.
Psychomotor Domain:
(a) Accurately draw and label graphs of two linear equations on graph paper.
Social Domain:
(a) Work cooperatively in pairs or groups to check and interpret each other’s graphs.

Reference Materials

The following resources was used in planning this lesson:

9 Years Basic Education Curriculum
Lagos State Unified Scheme of Work for Junior Secondary Schools
Cuemath – Simultaneous Equations – Meaning, Methods to Solve, Examples
Relevant Textbooks

Instructional Materials

The teacher will teach this lesson with the aid of:

Graph sheets
Rulers and pencils
Mathematical sets
Whiteboard and markers
Charts showing sample graphs of linear equations
Prepared examples of simultaneous equations

Rationale for the Lesson

This lesson enables pupils to visually understand the relationship between two linear equations by plotting and identifying their intersection point as the solution.

Prerequisite/Previous Knowledge

Pupils have previously learned how to draw straight-line graphs and solve simple linear equations in one variable.

Lesson Content/Board Summary

Graphical Solution of Simultaneous Equations

Simultaneous equations are two or more equations with two unknown variables that are true at the same time. The graphical method is used to find the point where the two lines intersect, which represents the solution of the equations.

Compiling Table of Values

Before drawing the graph of a linear equation, we must compile a table of values. This involves substituting different values of one variable (usually ( x )) into the equation to find the corresponding values of the other variable (usually ( y )).

Example 1:
Solve graphically the equations:

( y = 2x + 1 )
( y = x + 4 )

Step 1: Create tables of values for each equation.

x	-1	0	1	2
y = 2x + 1	-1	1	3	5

x	-1	0	1	2
y = x + 4	3	4	5	6

Step 2: Plot both lines on the same graph sheet.
Step 3: The point of intersection of the two lines gives the values of ( x ) and ( y ).
From the graph, the lines intersect at (3, 7).
Therefore, the solution is: ( x = 3, y = 7 ).

Solving Problems Involving Simultaneous Equations Graphically

To solve simultaneous linear equations graphically:

The following are the steps:

Write both equations in the form ( y = mx + c ).
Choose suitable values for ( x ) and compute ( y ) for each equation.
Draw a table of values for each equation.
Plot both sets of points on the same graph.
Draw straight lines through each set of points.
Identify the point where both lines meet.
The coordinates of this intersection point are the solution to the simultaneous equations.

Example 2:
Solve graphically:

( 2x + y = 6 )
( x + y = 4 )

Solution:
Rewrite both in terms of ( y ):

( y = 6 – 2x )
( y = 4 – x )

x	0	1	2	3
y = 6 – 2x	6	4	2	0

x	0	1	2	3
y = 4 – x	4	3	2	1

Plot both equations on the same graph.
The two lines intersect at (2, 2).
Hence, the solution is: ( x = 2, y = 2 ).

Teaching Methods/Instructional Techniques:

Discussion, Lecture, Explanation, Demonstration, Guided Practice, Group Work, Question and Answer

Instructional Procedures

To deliver this lesson, the teacher will adopt the following steps:

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: Teacher revises previous lessons on straight-line graphs and asks pupils how to find the equation of a straight line.
Pupils’ Activity: Pupils recall and respond with examples of linear equations.
Learning Point: Pupils recall how to draw straight-line graphs and prepare for the new concept.

Step 2: Explanation of Simultaneous Equations

Time: 10 minutes
Teaching Skill: Explanation
Teacher’s Activity: Teacher explains that simultaneous equations are equations that share common variables and are solved together.
Pupils’ Activity: Pupils listen attentively and ask questions for clarity.
Learning Point: Pupils understand what simultaneous equations mean.

Step 3: Compiling Table of Values

Time: 10 minutes
Teaching Skill: Demonstration
Teacher’s Activity: Teacher demonstrates how to choose values of ( x ) and compute corresponding ( y ) values to create a table for two equations.
Pupils’ Activity: Pupils participate by substituting values and writing results.
Learning Point: Pupils learn how to prepare tables of values for linear equations.

Step 4: Graphical Solution

Time: 10 minutes
Teaching Skill: Guided Practice
Teacher’s Activity: Teacher guides pupils to plot both equations on graph paper, showing how to locate the intersection point.
Pupils’ Activity: Pupils draw graphs on graph paper and identify points of intersection.
Learning Point: Pupils can graphically solve simultaneous equations by plotting and interpreting graphs.

Step 5: Note-Taking

Time: 5 minutes
Teaching Skill: Reinforcement
Teacher’s Activity: Teacher dictates or writes the board summary for pupils to copy.
Pupils’ Activity: Pupils copy the lesson summary into their notebooks.
Learning Point: Pupils have a written record for future reference.

Step 6: Evaluation/Review

Time: 3 minutes
Teaching Skill: Questioning
Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

Define simultaneous equations.
State the steps involved in solving simultaneous equations graphically.
From your graph, what is the solution to the equations ( y = 2x + 1 ) and ( y = x + 4 )?
Pupils’ Activity: Pupils respond orally or with written answers.
Learning Point: Pupils’ understanding of graphical solutions is assessed.

Step 7: Conclusion

Time: 2 minutes
Teaching Skill: Reinforcement
Teacher’s Activity: Teacher summarizes the lesson, emphasizing that the intersection point gives the solution to both equations.
Pupils’ Activity: Pupils listen and ask final questions.
Learning Point: Pupils understand that simultaneous equations can be solved graphically.

Lesson Keywords

Simultaneous Equations – equations with two unknowns solved together.
Graph – a visual representation of data using coordinates.
Intersection – point where two lines meet on a graph.
Variable – a letter that represents an unknown number.
Coordinate – a pair of values (x, y) showing a point’s position.

Differentiation

Teacher supports slower learners by providing pre-drawn grid templates and extra guidance, while advanced learners solve additional equations independently.

Note for teachers using this lesson plan

Ensure pupils use accurate scales on graph paper and label axes properly. Correct plotting mistakes promptly. Encourage neatness and clear identification of intersection points.