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Warm Up

Graph Systems of Linear Inequalities. Warm Up. Lesson Presentation. Lesson Quiz. ANSWER. ANSWER. Warm-Up. 1. Graph y ≤ x + 2. 2. Graph y ≥ | x |. Example 1. Graph the system of inequalities. y > –2 x – 5. Inequality 1. y < x + 3. Inequality 2. STEP 1.

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Warm Up

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  1. Graph Systems of Linear Inequalities Warm Up Lesson Presentation Lesson Quiz

  2. ANSWER ANSWER Warm-Up 1.Graphy ≤ x + 2. 2.Graphy ≥ | x |.

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

  4. STEP 1 Graph each inequality in the system. Use red for y > –2x – 5and bluefory≤ x + 3. STEP 2 Identify the region that is common to both graphs. It is the region that is shaded purple. Example 1 SOLUTION

  5. 2 y > – x + 4 3 Example 2 Graph the system of inequalities. 2x + 3y < 6 Inequality 1 Inequality 2

  6. STEP 1 Graph each inequality in the system. Use red for2x + 3y <6and bluefory > – x + 4. 2 3 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. Example 2 SOLUTION

  7. y > x + 4 Example 3 Graph the system of inequalities. y < 3 Inequality 1 Inequality 2

  8. STEP 1 Graph each inequality in the system. Use red for y ≤3and bluefor y > x + 4 . STEP 2 Identify the region that is common to both graphs. It is the region that is shaded purple. Example 3 SOLUTION

  9. 1 2.2x – y > 4 2 4x – y < 5 Guided Practice Graph the system of inequalities. 1. y < 3x – 2 y > – x + 4

  10. 4. y < 4 3. x + y > – 3 y >x – 5 –6x + y < 1 Guided Practice

  11. Example 4 SHOPPING A discount shoe store is having a sale, as described in the advertisement shown. • 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.

  12. STEP 1 Write a system of inequalities. Let xbe the regular footwear price and let ybe the sale price. From the information in the ad, you can write the following four inequalities. Example 4 SOLUTION 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.

  13. Example 4 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 yis between these values: 0.4(70) = 28 and 0.9(70) = 63 So, the value ofysatisfies28 ≤ y ≤ 63. ANSWER Therefore, footwear regularly priced at $70 sells for between $28 and $63, inclusive, during the sale.

  14. 7. What if? In Example 4, suppose the advertisement showed a range of discounts of 20% – 50% and a range of regular prices of $40 – $100. Guided Practice 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.

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

  16. ANSWER Lesson Quiz Graph the system of inequalities. 1. y>–x – 4 y< 2x + 2

  17. 2. 2x – 4y< 8 y < – x + 4 ANSWER 1 3 Lesson Quiz Graph the system of inequalities.

  18. 3. y > x + 2 y< 4 x < – 1 ANSWER Lesson Quiz Graph the system of inequalities.

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