220 likes | 544 Views
Ordered Pairs. 1-7. Pre-Algebra. Warm Up. Solve. 1. x 8 = 19. x = 27. a = 7. 2. 5 = a 2. n = 17. 3. 7 + n = 24. c = 13. 4. 3 c 7 = 32. y = 3. 5. 17 y + 7 = 58. Learn to write solutions of equations in two variables as ordered pairs . Vocabulary. ordered pair.
E N D
Ordered Pairs 1-7 Pre-Algebra
Warm Up Solve. 1.x 8 = 19 x = 27 a = 7 2. 5 = a 2 n = 17 3. 7 + n = 24 c = 13 4. 3c 7 = 32 y = 3 5. 17y + 7 = 58
Learn to write solutions of equations in two variables as ordered pairs.
Vocabulary ordered pair
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 $8 $1 Price of banner = + • 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
? 11= 11 ? 11 = 4(3) – 1 Determining 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 Substitute 3 for x and 11 for y. A solution since 11=11. (3, 11) is a solution.
? 3 = 4(10) – 1 ? 3 = 39 Determining 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 Substitute 10 for x and 3 for y. (10, 3) is not a solution.
? 43 = 4(11) – 1 ? 43 = 43 Determining 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 Substitute 11 for x and 43 for y. A solution since 43 = 43. (11, 43) is a solution.
? 38 = 5(7) + 3 ? 38 = 38 Example 1 Determine whether the ordered pair is a solution of y = 5x + 3. A. (7, 38) y = 5x + 3 Substitute 7 for x and 38 for y. (7, 38) is a solution.
? 17 = 5(9) + 3 ? 17 = 48 Example 2 Determine whether the ordered pair is a solution of y = 5x + 3. B. (9, 17) y = 5x + 3 Substitute 9 for x and 17 for y. (9, 17) is not a solution.
? 53 = 5(10) + 3 ? 53 = 53 Example 3 Determine whether the ordered pair is a solution of y = 5x + 3. C. (10, 53) y = 5x + 3 Substitute 10 for x and 53 for y. (10, 53) is a solution.
x 7x y (x, y) 1 2 3 4 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 7(1) 7 (1, 7) 7(2) 14 (2, 14) 7(3) 21 (3, 21) 7(4) 28 (4, 28)
m 1 2 3 4 6m – 5 n (m, n) Creating a Table of Ordered Pair Solutions Use the given values to make a table of solutions. B.n = 6m –5for m = 1, 2, 3, 4 6(4) – 5 6(1) – 5 6(2) – 5 6(3) – 5 1 7 13 19 (2, 7) (4, 19) (1, 1) (3, 13)
m 1 2 3 4 8m – 2 n (m, n) Example 5 Use the given values to make a table of solutions. B.n = 8m –2for m = 1, 2, 3, 4 8(4) – 2 8(1) – 2 8(2) – 2 8(3) – 2 6 14 22 30 (2, 14) (4, 30) (1, 6) (3, 22)
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 wis wholesale cost. A. What will be the sales price of a sweater with a wholesale cost of $48? p = 1.2(48) The price of the sweater before tax is $48. p = 57.6 The sweater is $48, and after tax it will cost $57.60, so (48, 57.60) is a solution of the equation.
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 wis wholesale cost. B. What will be the sales price of a jacket with a wholesale cost of $85? p = 1.2(85) The price of the jacket before tax is $85. p = 102 The jacket is $85.00, and after tax it will cost $102, so (85, 102) is a solution of the equation.
Example 6 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.
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