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HW: Pg. 152-153 #11-13, 15-27eoo, 35, 36, 39, 54

HW: Pg. 155 #2-18 eoe

Animated Activity OnlineSystems of Linear Inequalities:http://www.classzone.com/cz/books/algebra_2_2007_na/resources/applications/animations/explore_learning/chapter_3/dswmedia/7_6_LinearInequal.html

EXAMPLE 1Graph the system of inequalities.y > 2x 5Inequality 1y < x + 3Inequality 2

3.3 Graphing and Solving Systems of Linear Inequalities

EXAMPLE 1Graph a system of two inequalitiesSTEP 2Identify the region that is common to both graphs. It is the region that is shaded purple.SOLUTION

STEP 1Graph each inequality in the system. Use red for y > 2x 5 and blue for y x + 3.3.3 Graphing and Solving Systems of Linear Inequalities

EXAMPLE 2Graph the system of inequalities.2x + 3y < 6Inequality 1Inequality 2

3.3 Graphing and Solving Systems of Linear Inequalities

EXAMPLE 2Graph a system with no solutionSTEP 2Identify the region that is common to both graphs. There is no region shaded both red and blue. So, the system has no solution.

SOLUTIONSTEP 1Graph each inequality in the system. Use red for 2x + 3y < 6 and blue for

3.3 Graphing and Solving Systems of Linear Inequalities

EXAMPLE 3Graph a system with an absolute value inequalityGraph the system of inequalities.y < 3Inequality 1Inequality 2

3.3 Graphing and Solving Systems of Linear Inequalities

EXAMPLE 3Graph a system with an absolute value inequality

STEP 2Identify the region that is common to both graphs. It is the region that is shaded purple.SOLUTIONSTEP 1Graph each inequality in the system. Use red for y 3 and blue for

3.3 Graphing and Solving Systems of Linear Inequalities

GUIDED PRACTICEfor Examples 1, 2 and 3Graph the system of inequalities.1. y < 3x 2y > x + 42. 4x y < 5

GUIDED PRACTICEfor Examples 1, 2 and 33. x + y > 36x + y < 1

4. y < 4

3.3 Graphing and Solving Systems of Linear Inequalities

3.3 Graphing and Solving Systems of Linear Inequalities

EXAMPLE 4Solve a multi-step problemSHOPPINGA discount shoe store is having a sale, as described in the advertisement shown below. Use the information in the ad to write a system of inequalities for the regular footwear prices and possible sale prices. Graph the system of inequalities.

Use the graph to estimate the range of possible sale prices for footwear that is regularly priced at $70.3.3 Graphing and Solving Systems of Linear Inequalities

EXAMPLE 4Solve a multi-step problemSOLUTIONSTEP 1Write a system of inequalities. Let x be the regular footwear price and let y be the sale price. From the information in the ad, you can write the following four inequalities.x 20Regular price must be at least $20.x 80Regular price can be at most $80.y 0.4xSale price is at least (100 60)% = 40% of regular price.y 0.9xSale price is at most (100 10)% = 90% of regular price.

EXAMPLE 4Solve a multi-step problem

STEP 2Graph each inequality in the system. Then identify the region that is common to all the graphs. It is the region that is shaded.STEP 3Identify the range of possible sale prices for $70 footwear. From the graph you can see that when x = 70, the value of y is between these values:0.4(70) = 28 and 0.9(70) = 63So, the value of y satisfies 28 y 63.Therefore, footwear regularly priced at $70 sells for between $28 and $63, inclusive, during the sale.ANSWER

GUIDED PRACTICEfor Examples 45. In Example 4, suppose the advertisement showed a range of discounts of 20% 50% and a range of regular prices of $40 $100.a. Write and graph a system of inequalities for the regular footwear prices and possible sale prices.x 40Regular price must be at least $40.x 100Regular price can be at most $100.y 0.5xSale price is at least (100 50)% = 50% of regular price.y 0.8xSale price is at most (100 20)% = 80% of regular price.

Use the graph to estimate the range of possible sale prices for footwear that is regularly priced at $60.b.30 y 48ANSWER

Homework:Pg. 160-161 #33-49o, 51