Intermediate Algebra (11th edition)

(b)

✓ True ✓ False

The ordered pair is not a solution of the system, since it does not make both

equations true.

1 - 1, 7 2

11 = 11 34 = 36

- 3 + 14  11 - 1 + 35  36

31 - 12 + 2172  11 - 1 + 5172  36

3 x+ 2 y= 11 x+ 5 y= 36

x+ 5 y= 36

3 x+ 2 y= 11

SECTION 4.1 Systems of Linear Equations in Two Variables 211

NOW TRY
EXERCISE 1
Is the ordered pair a
solution of the system?

3 x- 2 y= 0

• x+ 2 y= 8

1 2, 5 2

NOW TRY

; 1 - 1, 7 2

OBJECTIVE 2 Solve linear systems by graphing. One way to find the solu-

tion set of a linear system of equations is to graph each equation and find the point

where the graphs intersect.

Solving a System by Graphing

Solve the system of equations by graphing.

(1)

(2)

To graph these linear equations, we plot several points for each line.

x+y= 5 2 x-y= 4

2 x- y= 4

x+ y= 5

NOW TRY EXAMPLE 2

EXERCISE 2
Solve the system of equations
by graphing.

x- y= 1

3 x- 2 y= 6

x

y

0

2

(4, 3)

x

y

0

(3, 2)

Common

solution

x + y = 5

2 x – y = 4

FIGURE 2

To be sure that is a solution of bothequations, we check by substituting 3 for

xand 2 for yin each equation.

CHECK (1) (2)

✓ True

✓ True

Since 1 3, 2 2 makes both equations true, 51 3, 2 26 is the solution set of the system.

4 = 4

5 = 5 6 - 2  4

3 + 2  5 2132 - 2  4

x+ y= 5 2 x- y= 4

1 3, 2 2

NOW TRY ANSWERS

1. no


2. 51 4, 3 26

NOW TRY

The intercepts are a

convenient choice.

Find a third ordered

pair as a check.

xy

05

50

23

xy

0

20

44

• 4

As shown in FIGURE 2, the graph suggests that the point of intersection is the ordered

pair 1 3, 2 2.