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QUARTER I
Week 8 – Day 2
Subject: MATH
Grade Level: 8
Date: __________________
Session: 1
Content Standard
Performance Standard
Competency
Demonstrates understanding of key concepts of factors of
polynomials, rational algebraic expressions, linear
equations and inequalities in two variables, systems of
linear equations and inequalities in two variables and
linear functions.
Is able to formulate real-life problems involving factors of
polynomials, rational algebraic expressions, linear
equations and inequalities in two variables, systems of
linear equations and inequalities in two variables and
linear functions, and solve these problems accurately
using a variety of strategies.
Competency 17: Graphs a system of linear equations in
two variables. (M8AL-Ih-1)
I. OBJECTIVES
Knowledge: 
Skills: 
Differentiates the graph of the systems of linear
equations in two variables;
Draws the graph of systems of linear equations in two
variables;
Attitude: 
II. CONTENT
Shows patience in graphing systems of linear
equations in two variables.
SYSTEMS OF LINEAR EQUATIONS IN TWO
VARIABLES AND THEIR GRAPHS
III. LEARNING RESOURCES
A. References
1. Teacher’s Guide
Pages
2. Learner’s
Materials Pages
3. Textbook Pages
4. Additional
Materials
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MMNHS – Siaton 4
Teacher’s Guide (TG) in Mathematics 8, 286-288
Learner’s Module (LM) in Math 8, pp. 254 - 260
Intermediate Algebra for Second Year, pp. 5-6.
Distance Learning Module, Mathematics 2. pp. 9 – 18.
Moving Ahead With Mathematics II, 1999. P 55*
Distance Learning Module
Graphing Board
Meterstick
Ruler
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5. Learning Resources
(LR) portal
B. Other Learning
Resources
https: //www.google.com
IV. PROCEDURES
A. Reviewing or
presenting the new
lesson
B. Establishing a
purpose for the lesson
ACTIVITY: Exploration
Note to the Teacher:
 Review on determining the quadrant and coordinates
of the given points.
- Students will be given Cartesian coordinate plane
with letters on corresponding points. See page 4 of
the Intermediate Algebra textbook.
( the activity will consume 3 mins.)
1. Group the students into 3.
2. Each group will have to construct their own coordinate
plane and graph each point on it. See page 4 letter B of
test yourself.
3. Every group will have to discuss their answer/s in front
Note: Lead the students to the concept of “straight line.”
C. Presenting examples
of the new lesson
ACTIVITY: GRAPHING LINEAR EQUATIONS IN
TWO VARIABLES
Consider the equation 2x + y = 4. Ordered pairs that
satisfy the equation can be found. For example , if y = 0, a
value for x by substituting 0 for y in the equation.
2x + 0 = 4
2x = 4
x=2
The ordered pair (2,0) is one of the solutions. Other
ordered pairs found in the same manner are (1,2),
(0,4),(3,-2),(4,-4). Plot and connect the points.
- You can form table of values then graph.
- Graph the result (see table of values)
- Guided questions will follow
D. Discussing new
concepts and
practicing new skills
#1
Prepared by: CALVIN S. IJE
MMNHS – Siaton 4
The teacher will instruct the students to do this:
Find three points that satisfy the equation y = 2x – 3
and graph the equation by drawing a line through these
points.
If x = 0
if y = 0
y = 2x – 3
y = 2x – 3
y = 2(0) – 3
0 = 2x – 3
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y=0–3
y = -3
2x = 3
3
x=2
(0, -3)
If x = 2
then y = 2x – 3
y = 2(2) – 3
y=4–3
y=1
3
(2, 0)
(2,1)
Have a Cartesian plane
on the board or graph
board.
This time students will be given a system of equations
like:
2x – y = 4
x – 2y = 1
then let them graph,
x – 2y = 1
2x – y = 4
E. Discussing new
concepts and
practicing new skills
#2
ACTIVITY: Solving systems of equation/s by
GRAPHING
Note: the class will be given system of linear equations in
two variables for them to solve and graph.
a. x – y = 9
x - y = -7 (key answer at the bottom)
Differentiates the previous graph with the 2nd graph.
The first graph intersect at one point while the other
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F. Developing Mastery
do not- it is parallel.
Consider the following systems of linear equations. Graph
each systems. Compare the resulting graph.
a. 2x – y = 1
b. 4x + y = -2
-2x + y = -1
x–y=5
x 0 1/2
y -1 0
x 0 1/2
y -1 0
x
y
x
y
G. Finding practical
applications of
concepts and skills in
daily living
H. Making
Generalizations and
abstractions about
the lesson
I. Evaluating learning
J. Additional
Prepared by: CALVIN S. IJE
MMNHS – Siaton 4
0
-2
0
-5
-1/2
0
5
0
( key answer at the bottom)
Linear equations use one or more variables where one
variable is dependent on the other. Almost any situation
where there is an unknown quantity can be represented by
a linear equation, like figuring out income over time,
calculating mileage rates, or predicting profit. Many
people use linear equations every day, even if they do the
calculations in their head without drawing a line graph.
Example:
Imagine that you are taking a taxi while on vacation. You
know that the taxi service charges P9 to pick your family
up from your hotel and another P0.5 per mile for the trip.
Without knowing how many miles it will be to each
destination, you can set up a linear equation that can be
used to find the cost of any taxi trip you take on your trip.
By using "x" to represent the number of miles to your
destination and "y" to represent the cost of that taxi ride,
the linear equation would be: y = 0.5x + 9.
Guide Questions for Generalization:
To solve linear equations graphically, find at least two
points in each equation and connect.
Do the following:
A. Graph each of the following equations. Use graph
Paper.
1. 2x – y = 4 and y = 2x
Let’s Check Your Understanding
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Activities for
application or
remediation
Draw the graphs of the system below.
a. y = x + 1 and y = x – 2
In what way are the three graphs alike?
In what aspect are they different?
V.
VI.
REMARKS
REFLECTION
A. No. of learners who
earned 80% in the
evaluation
B. No. of learners who
require additional
activities for remediation
C. Did the remedial
lessons work? No. of
learners who have caught
up the lesson
D. No. of learners who
continue to require
remediation
E. Which of my teaching
strategies worked well?
Why did these work?
F. What difficulties did I
encounter which my
principal and supervisor
help me solve?
Prepared by: CALVIN S. IJE
MMNHS – Siaton 4
A. __ No. Of learners who earned 80% in the evaluation
B. __ No. Of learners who require additional activities for
remediation
C. Did the remedial lessons work? __ No. Of learners
who have caught up the lesson.
D. __ No. Of learners who continue to require
remediation.
Strategies used that work well:
__ Group collaboration
__ Games
__ Powerpoint Presentation
__ Answering preliminary activities/exercises
__ Discussion
__ Case Method
__ Think-Pair-Share (TPS)
__ Rereading of Paragraphs/Poems/Stories
__ Differentiated Instruction
__ Role Playing/Drama
__ Discovery Method
__ Lecture Method
Why?
__ Complete Ims
__ Availability of Materials
__ Pupil’s eagerness to learn
__ Group member’s Cooperation in doing their tasks
__ Bullying among pupils
__ Pupil’s behavior/attitude
__ Colorful Ims
__ Unavailable technology
Equipment (AVR/LCD)
__ Science/Computer/Internet Lab
__ Additional Clerical works
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__ Reading Readiness
G. What innovation or
localized I used/discover
which I wish to share
with other teacher?
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MMNHS – Siaton 4
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ATTACHMENT
Session: 1 (1 day)
Content: Graphing a Linear Equation in Two Variables.
DISCUSSIONS:



Exactly one point in the plane is named by a given ordered pair of numbers.
Exactly one ordered pair of numbers names a given point in the plane.
With at least three points on the Cartesian plane can form a straight line.

A system of linear equations consists of two or more linear equations
made up of two or more variables such that all equations in the system are
considered simultaneously. You will find systems of equations in every
application of mathematics. They are a useful tool for discovering and
describing how behaviors or processes are interrelated. It is rare to find,
for example, a pattern of traffic flow that that is only affected by weather.
Accidents, time of day, and major sporting events are just a few of the
other variables that can affect the flow of traffic in a city. In this section,
we will explore some basic principles for graphing and describing the
intersection of two lines that make up a system of equations.
Prepared by: CALVIN S. IJE
MMNHS – Siaton 4
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SUPPLEMENTARY ACTIVITIES
Note: The activities included here will be used only when needed.
result.
Graph the following systems of linear equations and differentiate the
result.
a. x – 3y = 4
2x – y = -2
Prepared by: CALVIN S. IJE
MMNHS – Siaton 4
b. 6x + 4y = - 3
10y + 25x = 15
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KEY ANSWER
Discussing new concepts and practicing new skills #2
Note: the class will be given a system of linear equations in two variables for them to
solve and graph.
a.
x–y=9
b. x - y = -7
(no solution)
Developing Mastery
a. 2x – y = 1
-2x + y = -1
Prepared by: CALVIN S. IJE
MMNHS – Siaton 4
b. 4x + y = -2
x–y=5
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Evaluating Learning
A. Graph each of the following equations. Use graph Paper.
1. 2x – y = 4 and y = 2x
y = 2x
2x – y = 4
.
Prepared by: CALVIN S. IJE
MMNHS – Siaton 4
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Let’s Check Your Understanding
Draw the graphs of the following on one set of axes.
a. y = x + 1 and y = x – 2
y=x+1
y=x–2
In what way are the three graphs alike?
-
The 3 graphs rises to the right; their slopes are positive.
In what aspect are they different?
-
They differ on the value of their slopes, the bigger the slope/s the steeper the line.
Prepared by: CALVIN S. IJE
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Graph the following systems of linear equations and differentiate the result.
a. x – 3y = 4
2x – y = -2
b. 6x + 4y = - 3
10y + 25x = 15
2x – y = -2
10y + 25x = 15
x – 3y = 4
6x + 4y -3
Prepared by: CALVIN S. IJE
MMNHS – Siaton 4
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REFERENCES
A. DepEd INSTRUCTIONAL MATERIALS:
Intermediate Algebra for Second Year, pp. 5-6.
Distance Learning Module, Mathematics 2. pp. 9 – 18.
Mathematics Learner’s Module in Grade 8 (LM) in Math 8, pp. 254 - 260
B. INTERNET SOURCES:
www.google.ph.com
 Linear Equations Solved by Graphing,
Prepared by: CALVIN S. IJE
MMNHS – Siaton 4