Beginning Algebra, 11th Edition

The false result means that the equations

in the system have graphs that are parallel lines.

The system is inconsistent and has no solution, so

the solution set is See FIGURE 8.

NOW TRY

0.

10 = 6

260 CHAPTER 4 Systems of Linear Equations and Inequalities

x

y

0

3

3

x = 5 – 2y

2 x + 4y = 6

FIGURE 8

CAUTION It is a common error to give “false” as the solution of an inconsis-

tent system. The correct response is 0.

Solving a System with Dependent Equations by Substitution

Solve the system by the substitution method.

(1)

(2)

Begin by solving equation (1) for yto get Substitute for yin

equation (2) and solve the resulting equation.

(2)

Let from equation (1).

Distributive property

Add 12. Combine like terms.

This true result means that every solution of

one equation is also a solution of the other, so the

system has an infinite number of solutions. The

solution set is

A graph of the equations of this system is shown

in FIGURE 9.

NOW TRY

51 x, y 2 | 3 x- y= 46.

0 = 0

- 9 x+ 9 x- 12 =- 12

- 9 x+ 313 x- 42 =- 12 y= 3 x- 4

- 9 x+ 3 y=- 12

y= 3 x-4. 3 x- 4

- 9 x+ 3 y=- 12

3 x- y= 4

NOW TRY EXAMPLE 5

EXERCISE 5
Solve the system by the
substitution method.

• 10 x+ 2 y=- 12

5 x- y= 6

x

y

2

2

–4

0

3 x – y = 4

–9x + 3y = –12

FIGURE 9

CAUTION It is a common error to give “true” as the solution of a system of de-

pendent equations. Write the solution set in set-builder notation using the equation in

the system (or an equivalent equation) that is in standard form, with integer coeffi-

cients that have greatest common factor 1.

NOW TRY
EXERCISE 4
Use substitution to solve the
system.

y= 4 x- 8

8 x- 2 y= 1

NOW TRY ANSWERS

4. 0 5. 51 x, y 2 | 5 x-y= 66

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