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

Inequality Symbols > < > <

Example 1 Is the following a solution?

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?

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)

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

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

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

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

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

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

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

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

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 CDs?

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 times in one week?

Example 8 Tickets for the fall dance are $5 per 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 the committee cover its expense?

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 large pizzas and 8 pitcher of soft drink?

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?