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

Agenda Warm Up Problem of the Day Lesson Presentation Practice Activity Quiz

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

Problem of the Day A moving van travels 50 miles per hour. Use the equation y = 50x. How far will the van travel in 4.5 hours? 50(4.5) = 225 miles

Learn to write solutions of equations in two variables as ordered pairs.

Vocabulary ordered pair

A sign at the store reads “Birthday Banners $8 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.

Number of letters in name Price of banner $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

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

Determine If an Ordered Pair Is a Solution of an Equation Example 1A: Determine If an Ordered Pair Is a Solution of an Equation Determine whether the ordered pair is a solution of y = 4x – 1. A. (3, 11) y = 4x – 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.

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

Determine If an Ordered Pair Is a Solution of an Equation Example 1C: Determine If an Ordered Pair Is a Solution of an Equation Determine whether the ordered pair is a solution of y = 4x – 1. C. (11, 43) y = 4x – 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.

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

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

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

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

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

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

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

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 = 1.2w, 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.

Example 3 Continued A salesman wants to make a 20% profit on everything he sells. The equation for the sales price p is p = 1.2w, 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.

A. How much will a $22 item cost after sales tax? Try This: Example 3A 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 = 1.075p, 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.

B. How much will a $10 item cost after sales tax? Try This: Example 3B 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 = 1.075p, 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.

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

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