2-1 Ordered Pairs

Lesson PresentationLesson Presentation

2-1 Ordered Pairs

Practice Problems

Solve.

x = 27

a = 7

n = 17

c = 13

y = 3E. 17y + 7 = 58

D. 3c – 7 = 32

C. 7 + n = 24

B. 5 = a – 2

A. x – 8 = 19

2-1 Ordered Pairs

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

2-1 Ordered Pairs

Learn to write solutions of equations in two

variables as ordered pairs.

2-1 Ordered Pairs

Vocabulary

ordered pair

2-1 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 12players. Find the cost for a set of jerseys for each team.

Let y be the total cost of a set of jerseys and xbe the number of jerseys needed.

2-1 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

2-1 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).

2-1 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.

Simplify.

The order in which a solution is written is important. Always write x first, then y.

Helpful Hint

2-1 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

Simplify.

2-1 Ordered Pairs

Determine whether each ordered pair is a solution of y = 5x + 3.

Check It Out: Example 1A

(7, 38)

y = 5x + 3

38 = 5(7) + 3?

Substitute 7 for x and 38 for y.

38 = 38?

�

(7, 38) is a solution.

2-1 Ordered Pairs

Determine whether each ordered pair is a solution of y = 5x + 3.

Check It Out: Example 1B

(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.

2-1 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

2-1 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)

2-1 Ordered Pairs

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 2A

2-1 Ordered Pairs

Use the given values to make a table of solutions.

n = 8m – 2 for m = 1, 2, 3, 4

30

8(1) – 2 8(2) – 2 8(3) – 2

6 14 22

(1, 6) (2, 14) (3, 22) (4, 30)

8(4) – 2

m 1 2 3

8m – 2

n

(m, n)

4

Check It Out: Example 2B

2-1 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.

2-1 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.

2-1 Ordered Pairs

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.

Check It Out: Example 3A

How much will a $22 item cost after sales tax?

c = 1.075(22)

c = 23.65

After sales tax, the $22 item will cost $23.65, so (22, 23.65) is a solution to the equation.

The price of the item before tax is $22. Multiply.

2-1 Ordered Pairs

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.

Check It Out: Example 3B

How much will a $10 item cost after sales tax?

c = 1.075(10)

c = 10.75

After sales tax, the $10 item will cost $10.75, so (10, 10.75) is a solution to the equation.

The price of the item before tax is $10. Multiply.

2-1 Ordered Pairs

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