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Lesson 6 -6: Am I a Solution? Goal: Find solutions to inequalities of two Lesson 6 -6: Am I a Solution? Goal: Find solutions to inequalities of two variables

Inequality Symbols • > • < Inequality Symbols • > • <

Example 1 Is the following a solution? Example 1 Is the following a solution?

Example 2 Is the following a solution? Give an example of an ordered pair Example 2 Is the following a solution? Give an example of an ordered pair that would be a solution.

Example 3 Is the following a solution? Example 3 Is the following a solution?

Practice 1 Is the following a solution? (1, 2) (5, -4) (-6, 7) Practice 1 Is the following a solution? (1, 2) (5, -4) (-6, 7)

Practice 2 Is the following a solution? (2, 2) (-5, 3) (-9, 0) Practice 2 Is the following a solution? (2, 2) (-5, 3) (-9, 0)

Example 4 Determine which is a solution. y<x+1 {(-1, 0), (3, 2), (2, 5), Example 4 Determine which is a solution. y

Example 4 Continued (x, y) y<x+1 Solution Example 4 Continued (x, y) y

Example 5 Determine which is a solution. 3 x + 2 y < 12 Example 5 Determine which is a solution. 3 x + 2 y < 12 {(1, 6), (3, 0), (2, 2), (4, 3)}

Example 5 Continued (x, y) 3 x + 2 y < 12 Solution Example 5 Continued (x, y) 3 x + 2 y < 12 Solution

Practice 3 Determine which is a solution. y < 2 x {(2, 6), (0, Practice 3 Determine which is a solution. y < 2 x {(2, 6), (0, -1), (3, 5), (-1, -2)}

Practice 3 Continued (x, y) y < 2 x Solution Practice 3 Continued (x, y) y < 2 x Solution

Practice 4 Determine which is a solution. 2 x – 3 y > 6 Practice 4 Determine which is a solution. 2 x – 3 y > 6 {(3, 2), (-2, -4), (6, 2), (5, 1)}

Practice 4 Continued (x, y) 2 x – 3 y > 6 Solution Practice 4 Continued (x, y) 2 x – 3 y > 6 Solution

Example 6 Sally found a used bookstore that sells pre-owned DVDs and CDs. DVDs Example 6 Sally found a used bookstore that sells pre-owned DVDs and CDs. DVDs cost $9 each and CDs cost $7 each. Sally can spend no more than $35. Write an inequality.

Example 6 Continued. Does she have enough money to buy 2 DVDs and 3 Example 6 Continued. Does she have enough money to buy 2 DVDs and 3 CDs?

Example 7 Camille has no more than $20. 00 to spend each week for Example 7 Camille has no more than $20. 00 to spend each week for lunch and bus fare. lunch costs $3. 00 each day and bus fare is $0. 75 each ride. Write an inequality.

Example 7 Continued. Can Camille buy lunch 5 times and ride the bus 8 Example 7 Continued. Can Camille buy lunch 5 times and ride the bus 8 times in one week?

Example 8 Tickets for the fall dance are $5 person and $8 for couples. Example 8 Tickets for the fall dance are $5 person and $8 for couples. In order to cover expenses, at least $1200 worth of tickets must be sold. Write an inequality.

Example 8 Continued. If 100 single tickets and 125 couple tickets are sold, will Example 8 Continued. If 100 single tickets and 125 couple tickets are sold, will the committee cover its expense?

Practice 5 Coach Riley wants to take her softball team out for pizza after Practice 5 Coach Riley wants to take her softball team out for pizza after the game. A large pizza costs $12 each and a pitcher of soft drink is $3 each. She doesn’t want to spend more than $60.

Practice 5 Continued Write an inequality. Will the coach be able to buy 3 Practice 5 Continued Write an inequality. Will the coach be able to buy 3 large pizzas and 8 pitcher of soft drink?

Practice 6 Rita wants to spend at most $230 on a new clothes. The Practice 6 Rita wants to spend at most $230 on a new clothes. The skirts she wants to buy are $35 each and the blouses are $25 each.

Practice 6 Continued Write an inequality. Can Rita buy 4 skirts and 4 shirts? Practice 6 Continued Write an inequality. Can Rita buy 4 skirts and 4 shirts?