Ordered Pairs

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3-1
Ordered Pairs
Warm Up
Problem of the Day
Lesson Presentation
Course 3
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Warm Up Solve.
x 27
1. x ? 8 19
a 7
2. 5 a ? 2
n 17
3. 7 n 24
4. 3c ? 7 32
c 13
y 3
5. 17y 7 58
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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
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Learn to write solutions of equations in two
variables as ordered pairs.
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Vocabulary
ordered pair
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The company that makes team uniforms for a soccer
league charges a 20 fee for team artwork and 10
for each jersey. Dominics team has 14 players,
and Alyssas 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.
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20
10
of jerseys

total cost of jerseys


y 20 10 x
Dominics team
y 20 (10 14)
y 160
Alyssas team
y 20 (10 12)
y 140
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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).
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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
Substitute 3 for x and 11 for y.
A solution since 1111.
?
(3, 11) is a solution.
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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
Substitute 10 for x and 3 for y.
?
(10, 3) is not a solution.
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Check It Out Example 1A
Determine whether each ordered pair is a solution
of y 5x 3.
(7, 38)
y 5x 3
Substitute 7 for x and 38 for y.
?
(7, 38) is a solution.
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Check It Out Example 1B
Determine whether each ordered pair is a solution
of y 5x 3.
(9, 17)
y 5x 3
Substitute 9 for x and 17 for y.
?
(9, 17) is not a solution.
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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)
1 3
4
(1, 4)
2 3
5
(2, 5)
3 3
6
(3, 6)
4 3
7
(4, 7)
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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
6(1) 5
6(2) 5
6(3) 5
1
7
13
(2, 7)
(1, 1)
(3, 13)
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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 6
7
(1, 7)
2 6
8
(2, 8)
3 6
9
(3, 9)
4 6
10
(4, 10)
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Check It Out Example 2B
Use the given values to make a table of solutions.
n 8m 2 for m 1, 2, 3, 4
8(4) 2
8(1) 2
8(2) 2
8(3) 2
30
6
14
22
(2, 14)
(4, 30)
(1, 6)
(3, 22)
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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.
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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.
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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.
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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.
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Lesson Quiz Part I
Determine 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
yes
no
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)
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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?
c 15n 50 95