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HW: Pg. 152-153 #11-13, 15-27eoo, 35, 36, 39, 54
HW: Pg. 155 #2-18 eoe
Animated Activity Online
Systems 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 1
Graph the system of inequalities.
y > –2x – 5 Inequality 1
y < x + 3 Inequality 2
3.3 Graphing and Solving Systems of Linear Inequalities
EXAMPLE 1
Graph a system of two inequalities
STEP 2 Identify the region that is common to both graphs. It is the region that is shaded purple.
SOLUTION
STEP 1 Graph 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 2
Graph the system of inequalities.
2x + 3y < 6 Inequality 1
Inequality 22
43
y x
3.3 Graphing and Solving Systems of Linear Inequalities
EXAMPLE 2
Graph a system with no solution
STEP 2 Identify the region that is common to both graphs. There is no region shaded both red and blue. So, the system has no solution.
SOLUTION
STEP 1 Graph each inequality in the system. Use red for 2x + 3y < 6
and blue for 24
3y x
3.3 Graphing and Solving Systems of Linear Inequalities
EXAMPLE 3
Graph a system with an absolute value inequality
Graph the system of inequalities.
y < 3 Inequality 1
Inequality 24y x
3.3 Graphing and Solving Systems of Linear Inequalities
EXAMPLE 3
Graph a system with an absolute value inequality
STEP 2 Identify the region that is common to both graphs. It is the region that is shaded purple.
SOLUTION
STEP 1 Graph each inequality in the system. Use red for y ≤ 3
and blue for 4y x
3.3 Graphing and Solving Systems of Linear Inequalities
GUIDED PRACTICE for Examples 1, 2 and 3
Graph the system of inequalities.
1. y < 3x – 2
y > – x + 4
2.
4x – y < 5
12 4
2x y
GUIDED PRACTICE for Examples 1, 2 and 3
3. x + y > – 3
–6x + y < 1
4. y < 4
5y x
3.3 Graphing and Solving Systems of Linear Inequalities
3.3 Graphing and Solving Systems of Linear Inequalities
EXAMPLE 4
Solve a multi-step problemSHOPPING
A 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 4 Solve a multi-step problem
SOLUTION
STEP 1 Write 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 ≥ 20 Regular price must be at least $20.
x ≤ 80 Regular price can be at most $80.
y ≥ 0.4x Sale price is at least (100 – 60)% = 40% of regular price.
y ≤ 0.9x Sale price is at most (100 – 10)% = 90% of regular price.
EXAMPLE 4 Solve a multi-step problem
STEP 2 Graph each inequality in the system. Then identify the region that is common to all the graphs. It is the region that is shaded.
STEP 3 Identify 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) = 63
So, 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 PRACTICE for Examples 4
5. 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 ≥ 40 Regular price must be at least $40.
x ≤ 100 Regular price can be at most $100.
y ≥ 0.5x Sale price is at least (100 – 50)% = 50% of regular price.
y ≤ 0.8x Sale 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
