Pre-Algebra

1-7 Ordered Pairs

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

Pre-Algebra

1-7 Ordered Pairs

An ordered pair is the pair of plugged in numbers that makes and equation true.

Our goal is to find x and y numbers that plug into the equation and work. If they do, the ordered pair is a solution to the equation.

Is (7, 15) a solution? 15 = 7 + 8 15 = 15 Yes!

Is (6, 13) a solution? 13 = 6 + 8 13 = 14 No!

y = x + 8 (x, y) Ordered pair

y = x + 8(x, y)

Pre-Algebra

1-7 Ordered Pairs

Determine whether the ordered pair (3, 11) is a solution of y = 4x – 1.

Additional Example 1A: Determining If an Ordered Pair Is a Solution of an Equation

A. (3, 11)

y = 4x – 1

11 = 4(3) – 1 Substitute 3 for x and 11 for y.

11= 11 (3, 11) is a solution to y = 4x – 1.

A solution since 11=11.

x y

Pre-Algebra

1-7 Ordered Pairs

Determine whether the ordered pair (11, 3) is a solution of y = 4x – 1.

Additional Example 1B: Determining If an Ordered Pair Is a Solution of an Equation

B. (11, 3)

y = 4x – 1

3 = 4(11) – 1 Substitute 11 for x and 3 for y.

3 = 43 (11, 3) is not a solution to y = 4x – 1.

x y

Pre-Algebra

1-7 Ordered Pairs

Determine whether the ordered pair (7, 38) is a solution of y = 5x + 3.

Try This: Example 1A

A. (7, 38)

y = 5x + 3

38 = 5(7) + 3 Substitute 7 for x and 38 for y.

38 = 38 (7, 38) is a solution to y = 5x + 3.

x y

Pre-Algebra

1-7 Ordered Pairs

Determine whether the ordered pair (30, 9) is a solution of y = 3x + 3.

Try This: Example 1B

B. (30, 9)

y = 3x + 3

9 = 3(30) + 3 Substitute 30 for x and 9 for y.

9 = 93 (30, 9) is not a solution to y = 3x + 3.

x y

Pre-Algebra

1-7 Ordered Pairs

Use the given values to make a table of ordered pair solutions.

Additional Example 2A: Creating a Table of Ordered Pair Solutions

A. y = 7x for x = 1, 2, 3, 4

x 7x y (x, y)

1

2

3

4

7(1) 7 (1, 7)

7(2) 14 (2, 14)

7(3) 21 (3, 21)

7(4) 28 (4, 28)

These four ordered pairs are all solutions that make y = 7x work.

Pre-Algebra

1-7 Ordered Pairs

Use the given values to make a table of ordered pair solutions.

A. y = 6x – 3 for x = 1, 2, 3, 4

x 6x - 3 y (x, y)

1

2

3

4

6(1) – 3 = 6 – 3 = 3 (1, 3)

6(2) – 3 = 12 – 3 = 9 (2, 9)

6(3) – 3 = 18 – 3 = 15 (3, 15)

6(4) – 3 = 24 – 3 = 21 (4, 21)

Try This: Example 2A

These 4 ordered pairs are solutions that make y=6x-3 work.

Pre-Algebra

1-7 Ordered Pairs

Use the given values to make a table of ordered pair solutions.

B. y = 8x + 2 for x = 1, 2, 3, 4

34

8(1) + 2 8(2) + 2 8(3) + 2

10 18 26

(1, 10) (2, 18) (3, 26) (4, 34)

8(4) + 2

x 1 2 3

8x + 2

y

(x, y)

4

Try This: Example 2B

Pre-Algebra

1-7 Ordered Pairs

Partner QuestionsDetermine whether each ordered pair is a solution for 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, 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)