Unit 4 Day 1 Notes

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.

Determine whether each ordered pair is a solution of y = 4x – 1.

(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

(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.

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

(7, 38)

y = 5x + 3

38 = 5(7) + 3?

Substitute 7 for x and 38 for y.

38 = 38 ?

(7, 38) is a solution.

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

(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.

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

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

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)

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

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)