Course 3

3-1 Ordered Pairs

Warm UpSolve.

x = 27

a = 7

n = 17

c = 13

y = 35. 17y + 7 = 58

4. 3c 7 = 32

3. 7 + n = 24

2. 5 = a 21. x 8 = 19

Course 3

3-1 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 3

3-1 Ordered Pairs

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

TB P. 118-121

Course 3

3-1 Ordered Pairs

Vocabulary

ordered pair

Course 3

3-1 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 3

3-1 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 3

3-1 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 3

3-1 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 3

3-1 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 3

3-1 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

x x + 3 y (x, y)

1

2

3

4

1 + 3 4 (1, 4)

2 + 3 5 (2, 5)

3 + 3 6 (3, 6)

4 + 3 7 (4, 7)

A table of solutions can be set up vertically or horizontally.

Helpful Hint

Course 3

3-1 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) – 5 6(2) – 5 6(3) – 5

1 7 13

(1, 1) (2, 7) (3, 13)

m 1 2 3

6m – 5

n

(m, n)

Course 3

3-1 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 3

3-1 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 3

3-1 Ordered Pairs

Lesson Quiz: Part IDetermine whether each ordered pair is a solution of 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

yesno

x 4x – 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)

Course 3

3-1 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