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System of Linear inequalities in two variables

This document provides instructions for solving systems of linear inequalities in two variables by graphing. It defines a system of inequalities and explains that the solution is the region where the graphs of the inequalities overlap. A step-by-step process is outlined: 1) graph each inequality individually, 2) shade the appropriate half-plane, 3) the overlapping shaded regions represent the solution. An example system is graphed to demonstrate. Students will evaluate by being assigned a system to graph and answer related questions about the solution region.

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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 