Lesson Presentation

Practice Problems Solve. A. x – 8 = 19 x = 27 B. 5 = a – 2 a = 7 C. 7 + n = 24 n = 17 D. 3c – 7 = 32 c = 13 E. 17y + 7 = 58 y = 3

Practice Problem F A moving van travels 50 miles per hour. Use the equation y = 50x, where x represents the number of hours. How far will the van travel in 4.5 hours? 225 miles

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

Vocabulary ordered pair

The company that makes team uniforms for a soccer league charges a $20 fee for team artwork and $10 for each jersey. Dominic’s team has 14 players, and Alyssa’s team has 12 players. Find the cost for a set of jerseys for each team. Let y be the total cost of a set of jerseys and x be the number of jerseys needed.

• y = $20 + $10 • x Dominic’s team: y = $20 + ($10 • 14)‏ y = $160 total cost of jerseys $20 $10 + • # of jerseys = y = $20 + $10 • x Dominic’s team: y = $20 + ($10 • 14)‏ y = $160 Alyssa’s team: y = $20 + ($10 • 12)‏ y = $140

An ordered pair (x, y) is a pair of numbers that can be used to locate a point on a coordinate plane. A solution of a two-variable equation can be written as an ordered pair. The ordered pair (14, 160) is a solution because 160 = $20 + ($10 • 14). The ordered pair (12, 140) is a solution because 140 = $20 + ($10 • 12).

Determine whether each ordered pair is a solution of y = 4x – 1. Additional Example 1A: Deciding Whether an Ordered Pair Is a Solution of an Equation Determine whether each ordered pair is a solution of y = 4x – 1. (3, 11)‏ y = 4x – 1 11 = 4(3) – 1 ? Substitute 3 for x and 11 for y. 11 = 11  Simplify. (3, 11) is a solution. The order in which a solution is written is important. Always write x first, then y. Helpful Hint

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

Determine whether each ordered pair is a solution of y = 5x + 3. Check It Out: Example 1A Determine whether each ordered pair is a solution of y = 5x + 3. (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 each ordered pair is a solution of y = 5x + 3. Check It Out: Example 1B Determine whether each ordered pair is a solution of y = 5x + 3. (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.

Additional Example 2A: Creating a Table of Ordered Pair Solutions Use the given values to make a table of solutions. y = x + 3 for x = 1, 2, 3, 4 x x + 3 y (x, y)‏ A table of solutions can be set up vertically or horizontally. Helpful Hint 1 2 3 4 1 + 3 4 (1, 4)‏ 2 + 3 5 (2, 5)‏ 3 + 3 6 (3, 6)‏ 4 + 3 7 (4, 7)‏

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

Check It Out: Example 2A Use the given values to make a table of solutions. y = x + 6 for x = 1, 2, 3, 4 x x + 6 y (x, y)‏ 1 2 3 4 1 + 6 7 (1, 7)‏ 2 + 6 8 (2, 8)‏ 3 + 6 9 (3, 9)‏ 4 + 6 10 (4, 10)‏

Check It Out: Example 2B Use the given values to make a table of solutions. 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)‏

Additional Example 3A: Consumer Math Application A salesman marks up the price of everything he sells by 20%. The equation for the sales price p is p = 1.2w, where w is wholesale cost. 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. Multiply. p = 57.6 The $48 wholesale sweater will cost the customer $57.60, so (48, 57.60) is a solution of the equation.

Additional Example 3B: Consumer Math Application A salesman marks up the price of everything he sells by 20%. The equation for the sales price p is p = 1.2w, where w is wholesale cost. 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. Multiply. p = 102 The $85.00 wholesale jacket will cost the customer $102, so (85, 102) is a solution of the equation.

Check It Out: 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%, the equation for total cost is c = 1.075p, where p is the price before tax. How much will a $22 item cost after sales tax? c = 1.075(22) The price of the item before tax is $22. Multiply. c = 23.65 After sales tax, the $22 item will cost $23.65, so (22, 23.65) is a solution to the equation.

Check It Out: 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%, the equation for total cost is c = 1.075p, where p is the price before tax. How much will a $10 item cost after sales tax? c = 1.075(10) The price of the item before tax is $10. Multiply. c = 10.75 After sales tax, the $10 item will cost $10.75, so (10, 10.75) is a solution to the equation.

Assignments: 1.) Ch. 2-1 Review Packet Mon. 11-25 2.) Pg. 52 (1-24) Tues. 11-26 3.) 3 graphing sheets Wed. 11-27