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1 Sstems of Linear Inequalities SUGGESTED LEARNING STRATEGIES: Marking the Tet, Quickwrite, Create Representations. Graph each inequalit on the number lines and grids provided. M Notes ACTIVITY.7 Inequalit Graph all Graph all (, ) < College Board. All rights reserved. < and - 0. Compare and contrast the graphs ou made in the third row of the table. In our eplanation, compare the graphs to those in the first two rows and use the following words: dimension, halfline, half-plane, open, closed, and intersection. Unit Etensions of Linear Concepts 87
2 ACTIVITY.7 Sstems of Linear Inequalities M Notes ACADEMIC VOCABULARY A sstem of linear inequalities consists of two or more inequalities with the same variables. SUGGESTED LEARNING STRATEGIES: Create Representations, Graphic Organizer, Guess and Check, Group Presentation. On a coordinate grid, graph the solutions common to the inequalities and >. Solving a sstem of linear inequalities means finding all solutions that are common to all inequalities in the sstem.. For the sstem of inequalities below, complete the chart b deciding if each ordered pair is a solution. Eplain our answers. + > - - Ordered Pair Is it a solution? Wh or wh not? (-, -) (, ) (, -) (0, ) 00 College Board. All rights reserved.. Find two more solutions of the sstem in Item. 88 SpringBoard Mathematics with Meaning Algebra
3 Sstems of Linear Inequalities ACTIVITY.7 SUGGESTED LEARNING STRATEGIES: Close Reading, Visualization Since a sstem of inequalities has infinitel man solutions, ou can represent all solutions using a graph. To solve a sstem of inequalities, graph each inequalit on the same coordinate grid b shading a half-plane. The region that is the intersection of the two shaded half-planes represents all solutions of the sstem. M Notes EXAMPLE Solve the sstem of inequalities. + - > Step : First, graph +. To graph an inequalit, it ma be helpful to solve the inequalit for first. Step : Net, graph - >. 00 College Board. All rights reserved. Step : Determine the solution. The Solution is the double shaded region. Solution: The solution is the doubl shaded region shown in Step. When finding the solution to a sstem of inequalities, it is helpful to shade each inequalit with a different pattern or a different color. Unit Etensions of Linear Concepts 89
4 ACTIVITY.7 Sstems of Linear Inequalities M Notes SUGGESTED LEARNING STRATEGIES: Create Representations, Quickwrite, Group Discussion 6. Graph + > on the coordinate grid below The sstem in Item 6 is the same as the sstem in Item. Plot the points listed in Items and on the graph above. Where do the points that are solutions lie? Where do points that are not solutions lie? 8. Find the solutions to the sstems of inequalities b graphing. a College Board. All rights reserved. 90 SpringBoard Mathematics with Meaning Algebra
5 Sstems of Linear Inequalities ACTIVITY.7 SUGGESTED LEARNING STRATEGIES: Create Representations, Group Discussion b. + > 6 - < M Notes c. Describe how ou found the solutions for these sstems. 00 College Board. All rights reserved. 9. Find the solutions to the sstems of inequalities b graphing. a. > + - > 8 Unit Etensions of Linear Concepts 9
6 ACTIVITY.7 Sstems of Linear Inequalities M Notes SUGGESTED LEARNING STRATEGIES: Create Representations, Group Discussion, Guess and Check b. + < Compare and contrast the sstems in Items 9(a) and 9(b). CHECK YOUR UNDERSTANDING Write. Use our guess answers and check on notebook to find an paper. ordered Show our work.. Solve the sstem of linear inequalities. pair that is a solution to the sstem of > - inequalities. < MATHEMATICAL Wh is graphing the + < REFLECTION preferred method of. Solve the sstem in Item b graphing. Confirm that the ordered pair ou wrote in Item is a solution. Eplain. representing a solution to a sstem of linear inequalities? 00 College Board. All rights reserved. 9 SpringBoard Mathematics with Meaning Algebra
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