12.2 Graphing Systems of Linear Inequalities

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1 Name Class Date 1. Graphing Sstems of Linear Inequalities Essential Question: How do ou solve a sstem of linear inequalities? Resource Locker Eplore Determining Solutions of Sstems of Linear Inequalities A sstem of linear inequalities consists of two or more linear inequalities that have the same variables. The solutions of a sstem of linear inequalities are all the ordered pairs that make all the inequalities in the sstem true. Solve the sstem of equations b graphing. + 3 > A B C First look at + 3 > 3. The equation of the boundar line is. What are the -and -intercepts? The inequalit smbol is > so use a line. D Shade the boundar line for solutions that are greater than the inequalit. Houghton Mifflin Harcourt Publishing Compan E F G H Graph + 3 > Look at The equation of the boundar line is. What are the -and -intercepts? The inequalit smbol is so use a line. Module 1 57 Lesson

2 I Shade the boundar line for solutions that are less than the inequalit. J Graph on the same graph as + 3 > K L Identif the solutions. The are represented b the Check our answer b using a point in each region. Complete the table. shaded regions. Ordered Pair Satisfies + 3 > 3? Satisfies - + 6? (0, 0) In the overlapping shaded regions? (, 3) (, ) (-, 6) Reflect 1. Discussion Wh is (0, 0)a good point to use for checking the answer to this sstem of linear inequalities? Houghton Mifflin Harcourt Publishing Compan Module 1 5 Lesson

3 Eplain 1 Solving Sstems of Linear Inequalities b Graphing You can use a graph of a sstem of linear inequalities to determine and identif solutions to the sstem of linear inequalities. Eample 1 Graph the sstem of linear inequalities. Give two ordered pairs that are solutions and two that are not solutions. A > - 3 Solve the first inequalit for Graph the sstem. + > (0, 0) and (, ) are solutions. (-6, -) and (-, ) are not solutions. B > _ 3 - Solve the first inequalit for Graph the sstem > _ 3 - and are solutions. and are not solutions. Reflect. Is ( 6, 6) a solution of the sstem? Houghton Mifflin Harcourt Publishing Compan Your Turn Graph the sstem of linear inequalities. Give two ordered pairs that are solutions and two that are not solutions < > - + < Module 1 59 Lesson

4 Eplain Graphing Sstems of Inequalities with Parallel Boundar Lines If the lines in a sstem of linear equations are parallel, there are no solutions. However, if the boundar lines in a sstem of linear inequalities are parallel, the sstem ma or ma not have solutions. Eample Graph each sstem of linear inequalities. Describe the solutions. A < - 3 > + B > This sstem has no solution. The solutions are all points the parallel lines and on the line. Your Turn Graph each sstem of linear inequalities. Describe the solutions < Houghton Mifflin Harcourt Publishing Compan Module Lesson

5 Elaborate 7. Is it possible for a sstem of two linear inequalities to have ever point in the plane as solutions? Wh or wh not?. Discussion How would ou write a sstem of linear inequalities from a graph? 9. Essential Question Check-In How does testing specific ordered pairs tell ou that the solution ou graphed is correct? Evaluate: Homework and Practice 1. Match the inequalit with the correct boundar line. Answers ma be used more than once. a. = Online Homework Hints and Help Etra Practice Houghton Mifflin Harcourt Publishing Compan b. = 3 > - + _ 1 c. = d. = e. = > f. = 3 Module Lesson

6 Determine if the given point satisfies either equation and is a solution of the sstem of inequalities < > -10 ; (0, 0) 3. ; (.5, -1.5) 5_ Determine if the given point is a solution of the sstem of inequalities. If not, find a point that is.. (-9, ) 5. (6, -) (0, -) Graph the sstem of linear inequalities. Give two ordered pairs that are solutions and two that are not solutions. 7. > > Houghton Mifflin Harcourt Publishing Compan Module 1 55 Lesson

7 9. < < > < _ < < Houghton Mifflin Harcourt Publishing Compan Module Lesson

8 Graph each sstem of linear inequalities. Describe the solutions < _ _ _ _ < 6-3 9_ < 9_ Houghton Mifflin Harcourt Publishing Compan Module 1 55 Lesson

9 < > > H.O.T. Focus on Higher Order Thinking 3. Persevere in Problem Solving Write and graph a sstem of linear inequalities for which the solutions are all the points in the second quadrant, not including points on the aes Critical Thinking Can the solutions of a sstem of linear inequalities be the points on a line? Eplain. Houghton Mifflin Harcourt Publishing Compan 5. Eplain the Error A student was asked to graph the sstem < - and _ describe the solution set. The student gave the following + answer. Eplain what the student did wrong, then give the correct answer. The solutions are the same as the solutions of _ Module Lesson

10 Lesson Performance Task Successful stock market investors know a lot about inequalities. The know up to what point the are willing to accept losses, and at what point the are willing to lock in their profits and not subject their investments to additional risk. The often have these inequalities all mapped out at the time the purchase a stock, so the can tell instantl if the are sticking to their investment strateg. Graph the sstem of linear inequalities. Then describe the solution set and give two ordered pairs that are solutions and two that are not. Is there anthing particular to note about the shape of this sstem? < > > Houghton Mifflin Harcourt Publishing Compan Module Lesson

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