Course Ordered Pairs Warm Up Solve. x = 27 a = 7 n = 17 c = 13 y = y + 7 = c  7 = n = = a  2 1. x  8 = 19

Course Ordered Pairs Problem of the Day 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

Course Ordered Pairs Learn to write solutions of equations in two variables as ordered pairs. TB P

Course Ordered Pairs Vocabulary ordered pair

Course Ordered Pairs 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.

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

Course Ordered Pairs 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).

Course Ordered Pairs 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 (3, 11) y = 4x – 1 11 = 4(3) – 1 ? Substitute 3 for x and 11 for y. 11= 11 ? (3, 11) is a solution. A solution since 11=11. The order in which a solution is written is important. Always write x first, then y. Helpful Hint

Course Ordered Pairs (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 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

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

Course Ordered Pairs Use the given values to make a table of solutions. Additional Example 2B: Creating a Table of Ordered Pair Solutions n = 6m – 5 for m = 1, 2, 3 6(1) – 56(2) – 56(3) – (1, 1) (2, 7) (3, 13) m123 6m – 5 n (m, n)

Course Ordered Pairs 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. Additional Example 3A: Consumer Math Application What will be the sales price of a sweater with a wholesale cost of $48? p = 1.2(48) p = 57.6 The $48 wholesale sweater will cost the customer $57.60, so (48, 57.60) is a solution of the equation. The wholesale cost of the sweater before tax is $48. Multiply.

Course Ordered Pairs Additional Example 3B: Consumer Math Application What will be the sales price of a jacket with a wholesale cost of $85? p = 1.2(85) p = 102 The $85.00 wholesale jacket will cost the customer $102, so (85, 102) is a solution of the equation. The wholesale cost of the jacket before tax is $85. Multiply. 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.

Course Ordered Pairs Lesson Quiz: Part I Determine whether each ordered pair is a solution of y = 4x  (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 yesno x4x – 6y(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)

Course Ordered Pairs Lesson Quiz: Part II 4. A plumbing company charges $50 for a service call and $15 per hour. They went on a 3-hour job. How much did the company earn? Write the equation and solve. c = 15n + 50; $95