System of Linear inequalities in two variables

SYSTEM OF LINEAR INEQUALITIES
IN TWO VARIABLES

LEARNING COMPETENCY
Solves a system of linear in two
variables (M8AL-IIb-1)

SPECIFIC OBJECTIVES:
Solve system of linear inequalities by
graphing.

Activity 1 ( A LINE OR HALF OF A PLANE)
Directions:
Using Geogebra android or ios application,
draw the graphs of the following linear
equations and inequalities in two variables.

1. 3𝑥 + 𝑦 = 10
2. 5𝑥 − 𝑦 = 12
3. 2𝑥 + 3𝑦 = 15
4. 3𝑥 − 4𝑦 = 8
5. 4𝑥 + 7𝑦 = −8
6. 3𝑥 + 𝑦 < 10
7. 5𝑥 − 𝑦 > 12
8. 2𝑥 + 3𝑦 ≤ 15
9. 3𝑥 − 4𝑦 ≥ 8
10. 4𝑥 + 7𝑦 < −8
SET A SET B

Questions:
1. How did you graph each mathematical
statement?
2. Compare the graphs of each 3𝑥 + 𝑦 = 10
and 3𝑥 + 𝑦 < 10. What statements can you
make?
How about 5𝑥 − 𝑦 = 12 and 5𝑥 − 𝑦 > 12?
2𝑥 + 3𝑦 = 15 and 2𝑥 + 3𝑦 ≤ 15?
3. How can you differentiate the graphs of linear
equations and inequalities in two variables?

Questions:
4. How many solutions does a linear equation in
two variables have? How about linear
inequalities in two variables?
5. Suppose you draw the graphs of 3𝑥 + 𝑦 < 10
and 5𝑥 − 𝑦 > 12 in another Cartesian
coordinate plane. How would you describe their
graphs?
What ordered pairs would satisfy both
inequalities?

Process Questions:
1. Were you able to draw the graph of each
mathematical statement?
2. Were able to compare the graphs of linear
equations and inequalities in two variables?
3. Were you able to find the ordered pairs that
satisfy two linear inequalities?

An ordered pair (𝑥, 𝑦) is a solution to a system of
inequalities if it satisfies all the inequalities in the
system.
Graphically, the coordinates of a point that lie on
the graphs of all inequalities in the system is part of
its solution.

How are we going to solve a system of inequalities
in two variables by graphing?

Steps solving system of inequalities in two
variables by graphing:
1. Draw the graph of each inequality on the same
coordinate plane. (use x-y intecepts)
2. Choose at least two points/ coordinates on the
plane and set as a test point/s inorder to
determine the solution of the inequality.
3. Shade the appropriate half-plane.
4. The region where shaded areas overlap is the
graphical solution to the system. If the graph do
not overlap, the the system has no solution.

Graph the system
2𝑥 + 5𝑦 < 10
𝑥 − 𝑦 ≥ −8
Example:
1. Draw the graph of the system
2𝑥 + 5𝑦 < 10
𝑥 − 𝑦 ≥ −8
Step by step procedure:

Example:
1. Draw the graph of the
inequalities
1.1 Draw the graph of
the first inequality
2𝑥 + 5𝑦 < 10

2. Choose a test point to
determine the half-
plane of the
inequalities.
Example: 0, 0
2𝑥 + 5𝑦 < 10
2 0 + 5 0 < 10
0 < 10 TRUE
•

Draw the graph of the
inequalities
1.1 Draw the graph of
the first inequality
𝑥 − 𝑦 ≥ −8

2. Choose a test point to
determine the half-
plane of the inequalities.
Example: 4, −2
𝑥 − 𝑦 ≥ −8
4 − −2 ≥ −8
4 + 2 ≥ −8
6 ≥ −8 TRUE
•

1.3 The graph of the
inequalities must be in
the same coordinate
plane
2𝑥 + 5𝑦 < 10
𝑥 − 𝑦 ≥ −8

4. The region where
shaded areas overlap is
the graphical solution
to the system. If the
graph do not overlap,
the the system has no
solution.

Application:
Solve the system by graphing:
2𝑥 − 𝑦 ≥ 10
2𝑦 ≥ 5𝑥 + 1

Evaluation: ( Group Activity)
Each group will be given a strip of paper with
system inequalities. Answer what is asked in each
system.
Group 1. Do and Satisfy Me (LM p. 295)
Group 2. Region in A Plane (LM p. 296)
Group 3. Am I in that Region?
(LM p. 297 answer no. 2)

Rubrics:
CRITERIA Outstanding
(5)
Satisfactory
(4)
Developing
(3)
Beginning
(2)
Reasoning Explanation of
the system of
inequalities
shows reasoning
and justification.
Explanation
shows
substantial
reasoning
Explanation
shows gaps in
reasoning
Explanation
shows illogical
reasoning
Accuracy All graphs are
correct and
shown in detail
All graphs are
correct
Most
computations
are correct
Some
computations
are correct.
Presentation Presentation is
delivered in a
convincing
manner
Presentation is
delivered in a
clear manner
Presentation is
delivered in a
disorganized
manner

Thank you very much for
listening and cooperating!!!
-Maam Charina 

System of Linear inequalities in two variables

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System of Linear inequalities in two variables