Intermediate Algebra (11th edition)

254 CHAPTER 4 Systems of Linear Equations

1.Asystem of equationsconsists of
A.at least two equations with
different variables
B.two or more equations that have
an infinite number of solutions
C.two or more equations that are to
be solved at the same time
D.two or more inequalities that are
to be solved.

2.Thesolution set of a system of
equationsis
A.all ordered pairs that satisfy one
equation of the system
B.all ordered pairs that satisfy all
the equations of the system at the
same time

C.any ordered pair that satisfies

one or more equations of the

system

D.the set of values that make all the

equations of the system false.

3.Aninconsistent systemis a system

of equations

A.with one solution

B.with no solution

C.with an infinite number of

solutions

D.that have the same graph.

4. Dependent equations
   A.have different graphs
   B.have no solution

C.have one solution

D. are different forms of the same

equation.

5.Amatrixis

A.an ordered pair of numbers

B.an array of numbers with the

same number of rows and

columns

C.a pair of numbers written

between brackets

D.a rectangular array of numbers.

TEST YOUR WORD POWER

See how well you have learned the vocabulary in this chapter.

ANSWERS

1.C;Example: 2.B;Example:The ordered pair satisfies both equations of the system in Answer 1, so is the solution set

of the system. 3.B;Example:The equations of two parallel lines form an inconsistent system. Their graphs never intersect, so the system has
no solution. 4.D;Example:The equations and are dependent because their graphs are the same line.

5.D;Examples:c
3
4

• 1
  2

0

1

d,c

1

4

2

3

d

4 x-y= 8 8 x- 2 y= 16

1 2, 3 2 51 2, 3 26

3 x-y= 3

2 x+y= 7

4.1 Systems of Linear Equations in Two

Variables

Solving a Linear System by Substitution

Step 1 Solve one of the equations for either variable.

Step 2 Substitute for that variable in the other equation.
The result should be an equation with just one
variable.

Step 3 Solve the equation from Step 2.

Step 4 Find the value of the other variable by substi-
tuting the result from Step 3 into the equation
from Step 1.

Step 5 Check the ordered-pair solution in bothof the
originalequations. Then write the solution set.

Solve by substitution.

(1)

(2)

Solve for yin equation (1):.

Substitute for yin equation (2), and solve for x.

(2)

Let

Distributive property

Combine like terms. Add 14.

Divide by 11.

Substitute 4 for x in the equation to find that

Check to see that 514 , 926 is the solution set.

y= 4142 - 7 = 9.

y= 4 x- 7

x= 4

11 x= 44

3 x+ 8 x- 14 = 30

3 x+ 214 x- 72 = 30 y= 4 x-7.

3 x+ 2 y= 30

4 x- 7

y= 4 x- 7

3 x+ 2 y= 30

4 x- y= 7

QUICK REVIEW

CONCEPTS EXAMPLES

(continued)