Beginning Algebra, 11th Edition

OBJECTIVE 3 Decide whether a given ordered pair is a solution of a

given equation. We substitute the x-and y-values of an ordered pair into a linear

equation in two variables to see whether the ordered pair is a solution. An ordered

pair that is a solution of an equation is said to satisfythe equation.

178 CHAPTER 3 Linear Equations and Inequalities in Two Variables; Functions

CAUTION The ordered pairs and are notthe same. In the first

pair, and In the second pair, and The order in which

the numbers are written in an ordered pair is important.

x= 2 y=13. x= 13 y=2.

12 , 132 113 , 22

NOW TRY
EXERCISE 2
Decide whether each ordered
pair is a solution of the equa-
tion.

(a) 1 3, 4 2 (b) 1 - 3, - 42

3 x- 7 y= 19

Deciding Whether Ordered Pairs Are Solutions of an Equation

Decide whether each ordered pair is a solution of the equation

(a)

Substitute 3 for xand 2 for yin the equation.

Let and.

Multiply.

✓ True

This result is true, so is a solution of

(b)

Let and.

Multiply.

False

This result is false, so 1 - 2, - 72 is nota solution of 2 x+ 3 y=12. NOW TRY

- 25 = 12

- 4 + (-21) 12

21 - 22 + 31 - 72  12 x=- 2 y=- 7

2 x+ 3 y= 12

1 - 2, - 72

1 3, 2 2 2 x+ 3 y=12.

12 = 12

6 + 6  12

2132 + 3122  12 x= 3 y= 2

2 x+ 3 y= 12

1 3, 2 2

2 x+ 3 y=12.

EXAMPLE 2

Use parentheses to

avoid errors.

OBJECTIVE 4 Complete ordered pairs for a given equation. Substituting a

number for one variable in a linear equation makes it possible to find the value of the

other variable.

Completing Ordered Pairs

Complete each ordered pair for the equation

(a)

In this ordered pair,. To find the corresponding value of y, replace xwith 7

in the equation.

Let

Multiply.

Add.

The ordered pair is 17 , 332.

y= 33

y= 28 + 5

y= 4172 + 5 x=7.

y= 4 x+ 5

x= 7

1 7,^2

y= 4 x+5.

EXAMPLE 3

The x-value always comes first.

NOW TRY ANSWERS

2. (a)no (b)yes

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