Beginning Algebra, 11th Edition

248 CHAPTER 4 Systems of Linear Equations and Inequalities

OBJECTIVES A system of linear equations,often called a linear system,consists of two or more

linear equations with the same variables.

Linear systems

3 x- y=- 5 - y= 4 - 2 x y= 3

2 x+ 3 y= 4 x+ 3 y= 1 x- y= 1

Solving Systems of Linear Equations by Graphing

4.1

1 Decide whether a

given ordered pair

is a solution of a

system.

2 Solve linear systems

by graphing.

3 Solve special

systems by

graphing.

4 Identify special

systems without

graphing.

NOTE In the system on the right, think of as an equation in two variables by

writing it as 0 x+ y=3.

y= 3

OBJECTIVE 1 Decide whether a given ordered pair is a solution of a

system. A solution of a systemof linear equations is an ordered pair that makes

both equations true at the same time. A solution of an equation is said to satisfythe

equation.

Determining Whether an Ordered Pair Is a Solution

Decide whether the ordered pair is a solution of each system.

(a)

To decide whether is a solution of the system, substitute 4 for xand

for yin each equation.

Substitute. Substitute.

Multiply. Multiply.

✓ True ✓ True

Because satisfies both equations, it is a solution of the system.

(b)

Again, substitute 4 for xand for yin both equations.

Substitute. Substitute.

Multiply. Multiply.

✓ True False

The ordered pair is not a solution of this system because it does not satisfy

the second equation. NOW TRY

OBJECTIVE 2 Solve linear systems by graphing. The set of all ordered

pairs that are solutions of a system is its solution set.One way to find the solution

set of a system of two linear equations is to graph both equations on the same axes.

1 4, - 32

- 7 =- 7 0 = 2

8 + 1 - 152 - 7 12 + 1 - 122  2

2142 + 51 - 32 - 7 3142 + 41 - 32  2

2 x+ 5 y=- 7 3 x+ 4 y= 2

- 3

3 x+ 4 y= 2

2 x+ 5 y=- 7

1 4, - 32

- 8 =- 8 6 = 6

4 + 1 - 122 - 8 12 + 1 - 62  6

4 + 41 - 32 - 8 3142 + 21 - 32  6

x+ 4 y=- 8 3 x+ 2 y= 6

1 4, - 32 - 3

3 x+ 2 y= 6

x+ 4 y=- 8

1 4, - 32

NOW TRY EXAMPLE 1

EXERCISE 1
Decide whether the ordered
pair is a solution of
each system.

(a)

(b)

2 x+y= 12

3 x-y= 13

x- y= 7

2 x+ 5 y= 20

1 5, 2 2

NOW TRY ANSWERS

1. (a)no (b)yes

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