1 7 Ordered Pairs Chapter 1 Algebra Toolbox

1 -7 Ordered Pairs Chapter 1 Algebra Toolbox 1 -7 Ordered Pairs Objective: write solutions of equations in two variables as ordered pairs

1 -7 Ordered Pairs Agenda Warm Up Problem of the Day Lesson Presentation Practice Activity Quiz

1 -7 Ordered Pairs Warm Up Solve. 1. x 8 = 19 2. 5 = a 2 3. 7 + n = 24 4. 3 c 7 = 32 5. 17 y + 7 = 58 x = 27 a=7 n = 17 c = 13 y=3

1 -7 Ordered Pairs Problem of the Day A moving van travels 50 miles per hour. Use the equation y = 50 x. How far will the van travel in 4. 5 hours? 50(4. 5) = 225 miles

1 -7 Ordered Pairs Learn to write solutions of equations in two variables as ordered pairs.

1 -7 Ordered Pairs Vocabulary ordered pair

1 -7 Ordered Pairs A sign at the store reads “Birthday Banners $8. Personalize for $1 per letter. ” Cecilia has 7 letters in her name, and Dowen has 5 letters in his. Figure out how much it will cost to get a personalized birthday banner for each of them.

1 -7 Price of banner Ordered Pairs = $8 + $1 • Number of letters in name Let y be the price of the banner and x be the number of letters in the name; the equation for the price of a banner is y = 8 + x. For Cecelia’s banner: x = 7, y = 8 + 7 or y = 15 For Dowen’s banner: x = 5, y = 8 + 5 or y = 13

1 -7 Ordered Pairs A solution of a two-variable equation is written as an ordered pair. When the numbers in the ordered pair are substituted in the equation, the equation is true. (7, 15) is a solution 15 = 7 + 8 (5, 13) is a solution 13 = 5 + 8 (x, y) Ordered pair

1 -7 Ordered Pairs Example 1 A: Determine If an Ordered Pair Is a Solution of an Equation Determine whether the ordered pair is a solution of y = 4 x – 1. A. (3, 11) y = 4 x – 1 ? 11 = 4(3) – 1 Substitute 3 for x and 11 for y. ? 11= 11 A solution since 11=11. (3, 11) is a solution.

1 -7 Ordered Pairs Example 1 B: Determine If an Ordered Pair Is a Solution of an Equation Determine whether the ordered pair is a solution of y = 4 x – 1. B. (10, 3) y = 4 x – 1 ? 3 = 4(10) – 1 ? 3 = 39 Substitute 10 for x and 3 for y. (10, 3) is not a solution.

1 -7 Ordered Pairs Example 1 C: Determine If an Ordered Pair Is a Solution of an Equation Determine whether the ordered pair is a solution of y = 4 x – 1. C. (11, 43) y = 4 x – 1 ? 43 = 4(11) – 1 Substitute 11 for x and 43 for y. ? 43 = 43 A solution since 43 = 43. (11, 43) is a solution.

1 -7 Ordered Pairs Try This: Example 1 A Determine whether the ordered pair is a solution of y = 5 x + 3. A. (7, 38) y = 5 x + 3 ? 38 = 5(7) + 3 Substitute 7 for x and 38 for y. ? 38 = 38 (7, 38) is a solution.

1 -7 Ordered Pairs Try This: Example 1 B Determine whether the ordered pair is a solution of y = 5 x + 3. B. (9, 17) y = 5 x + 3 ? 17 = 5(9) + 3 Substitute 9 for x and 17 for y. ? 17 = 48 (9, 17) is not a solution.

1 -7 Ordered Pairs Try This: Example 1 C Determine whether the ordered pair is a solution of y = 5 x + 3. C. (10, 53) y = 5 x + 3 ? 53 = 5(10) + 3 Substitute 10 for x and 53 for y. ? 53 = 53 (10, 53) is a solution.

1 -7 Ordered Pairs Example 2 A: Creating a Table of Ordered Pair Solutions Use the given values to make a table of solutions. A. y = 7 x for x = 1, 2, 3, 4 x 7 x y (x, y) 1 7(1) 7 (1, 7) 2 7(2) 14 (2, 14) 3 7(3) 21 (3, 21) 4 7(4) 28 (4, 28)

1 -7 Ordered Pairs Example 2 B: Creating a Table of Ordered Pair Solutions Use the given values to make a table of solutions. B. n = 6 m – 5 for m = 1, 2, 3, 4 m 1 2 3 4 6 m – 5 6(1) – 5 6(2) – 5 6(3) – 5 6(4) – 5 n 1 7 13 19 (m, n) (1, 1) (2, 7) (3, 13) (4, 19)

1 -7 Ordered Pairs Try This: Example 2 A Use the given values to make a table of solutions. A. y = 6 x for x = 1, 2, 3, 4 x 6 x y (x, y) 1 6(1) 6 (1, 6) 2 6(2) 12 (2, 12) 3 6(3) 18 (3, 18) 4 6(4) 24 (4, 24)

1 -7 Ordered Pairs Try This: Example 2 B Use the given values to make a table of solutions. B. n = 8 m – 2 for m = 1, 2, 3, 4 m 1 2 3 4 8 m – 2 8(1) – 2 8(2) – 2 8(3) – 2 8(4) – 2 n 6 14 22 30 (m, n) (1, 6) (2, 14) (3, 22) (4, 30)

1 -7 Ordered Pairs Example 3: Retail Application A salesman wants to make a 20% profit on everything he sells. The equation for the sales price p is p = 1. 2 w, where w is wholesale cost. A. What will be the sales price of a sweater with a wholesale cost of $48? p = 1. 2(48) The wholesale cost of the sweater before tax is $48. p = 57. 6 The $48 wholesale sweater will cost the customer $57. 60, so (48, 57. 60) is a solution of the equation.

1 -7 Ordered Pairs Example 3 Continued A salesman wants to make a 20% profit on everything he sells. The equation for the sales price p is p = 1. 2 w, where w is wholesale cost. B. What will be the sales price of a jacket with a wholesale cost of $85? p = 1. 2(85) The wholesale cost of the jacket before tax is $85. p = 102 The $85 wholesale jacket will cost the customer $102, so (85, 102) is a solution of the equation.

1 -7 Ordered Pairs Try This: Example 3 A In most states, the price of each item is not the total cost. Sales tax must be added. If sales tax is 7. 5 percent, the equation for total cost is c = 1. 075 p, where p is the price before tax. A. How much will a $22 item cost after sales tax? c = 1. 075(22) The price of the item before tax is $22. c = 23. 65 After sales tax, the $22 item will cost $23. 65, so (22, 23. 65) is a solution to the equation.

1 -7 Ordered Pairs Try This: Example 3 B In most states, the price of each item is not the total cost. Sales tax must be added. If sales tax is 7. 5 percent, the equation for total cost is c = 1. 075 p, where p is the price before tax. B. How much will a $10 item cost after sales tax? c = 1. 075(10) The price of the item before tax is $10. c = 10. 75 After sales tax, the $10 item will cost $10. 75, so (10, 10. 75) is a solution to the equation.

1 -7 Ordered Pairs Lesson Quiz Determine whether each ordered pair is a solution for y = 4 x 7. 1. (2, 15) no 2. (4, 9) yes 3. Use the given values to make a table of solutions. y = 4 x 6 for x = 2, 4, 6, 8, and 10 x 4 x – 6 y (x, y) 2 4(2) 6 2 (2, 2) 4 4(4) 6 10 (4, 10) 6 4(6) 6 18 (6, 18) 8 4(8) 6 26 (8, 26) 10 4(10) 6 34 (10, 34)

1 -7 Ordered Pairs Let’s try some!