Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Algebra 2 - Chapter 3 Review

Solve the system by graphing.

____ 1. 3x 2y 7

3x y 10

a.

(3, –1)

c.

(–1, 3)b.

(1, 3)

d.

(3, 1)

Name: ________________________ ID: A

2

____ 2. 4x y 12

4x 4y 8

a.

(–2, –4)

c.

(–2, 4)b.

(4, –2)

d.

(–4, –2)

Without graphing, is each system independent, dependent, or inconsistent?

____ 3. x 5y 7

4x y 7

a. inconsistent c. dependentb. independent

____ 4. y 4x 6

8x 2y 12

a. independent c. dependentb. inconsistent

Name: ________________________ ID: A

3

Solve the system by substitution.

____ 5. 2x y 14

3x y 11

a. (–4, –5) c. (–5, –4)b. (5, 4) d. (4, 5)

____ 6. 2.5x y 13.5

2.25x y 12.25

a. (–5, 1) c. (1, –5)b. (–1, 5) d. (5, –1)

Solve the system using elimination.

____ 7. 4x 4y 8

x 4y 7

a. (3, 5) c. (–3, –5)b. (5, 3) d. (–5, –3)

____ 8. 7x 2y 11

4x 7y 10

a. (–2, –1) c. (–1, –2)b. (2, 1) d. (1, 2)

What are the solutions of the following systems?

____ 9. x 2y 10

3x 6y 11

a. infinitely many solutions c. (5, –2)b. (–5, 2) d. no solutions

____ 10. x 3y 9

x 3y 9

a. (5, –6) c. (–5, 6)b. no solutions d. infinitely many solutions

Name: ________________________ ID: A

4

____ 11. A group of 36 people attended a ball game. There were twice as many children as adults in the group. Set up a system of equations that represents the numbers of adults and children who attended the game and solve the system to find the number of adults and the number of children who were in the group.

a.a c 36

c 2a

; 12 adults, 24 children c.a c 36

a c 2

; 24 adults; 17 children

b.a c 36

c a 2

; 17 adults; 24 children d.a c 36

a 2c

; 24 adults, 12 children

____ 12. The length of a rectangle is 6.7 cm more than 2 times the width. If the perimeter of the rectangle is 57.2 cm, what are its dimensions?

a. length = 21.3 cm; width = 7.3 cm c. length = 7.3 cm; width = 21.3 cmb. length = 21.3 cm; width = 14 cm d. length = 7.9 cm; width = 14 cm

Name: ________________________ ID: A

5

Solve the system of inequalities by graphing.

____ 13. y 3x 1

y 3x 2

a. c.

b. d.

Name: ________________________ ID: A

6

____ 14. x 2

y 1

a. c.

b. d.

Name: ________________________ ID: A

7

____ 15. y 3x 1

y 12

x 1

a. c.

b. d.

Name: ________________________ ID: A

8

Solve the system of inequalities by graphing.

____ 16. y 4

y x 1

a. c.

b. d.

Name: ________________________ ID: A

9

____ 17. y x

y 3x 2 5

a. c.

b. d.

Name: ________________________ ID: A

10

____ 18. Your club is baking vanilla and chocolate cakes for a bake sale. They need at most 27 cakes. You cannot have more than 13 chocolate cakes. Write and graph a system of inequalities to model this system.

a. Let x = the number of vanilla cakes.Let y = the number of chocolate cakes.

x 0

y 0

x y 27

y 13

c. Let x = the number of vanilla cakes.Let y = the number of chocolate cakes.

x 0

y 0

x y 27

y 13

b. Let x = the number of vanilla cakes.Let y = the number of chocolate cakes.

x 0

y 0

x y 27

y 13

d. Let x = the number of vanilla cakes.Let y = the number of chocolate cakes.

x 0

y 0

x y 27

y 13

Name: ________________________ ID: A

11

____ 19. An exam consists of two parts, Section X and Section Y. There can be a maximum of 80 questions. There must be at least 10 more questions in Section Y than in Section X. Write a system of inequalities to model the number of questions in each of the two sections. Then solve the system by graphing.

a.

X 0

Y 0

X Y 80

Y X 10

c.

X 0

Y 0

X Y 80

Y X 10

b.

X 0

Y 0

X Y 80

Y X 10

d.

X 0

Y 0

X Y 80

Y X 10

Name: ________________________ ID: A

12

What point in the feasible region maximizes the objective function?

____ 20. Constraints

x 0

y 0

x 5 y

y 13

x 3

Objective function: C 4x 4y

a. (5,0) c. (0,0)b. (1.5,3.5) d. (0,3)

ID: A

1

Algebra 2 - Chapter 3 ReviewAnswer Section

1. ANS: A PTS: 1 DIF: L2 REF: 3-1 Solving Systems Using Tables and Graphs OBJ: 3-1.1 To solve a linear system using a graph or a table NAT: CC A.CED.2| CC A.CED.3| CC A.REI.6| CC A.REI.11| A.4.d TOP: 3-1 Problem 1 Using a Graph or Table to Solve a System KEY: system of linear equations | graphing | solution of a system

2. ANS: A PTS: 1 DIF: L2 REF: 3-1 Solving Systems Using Tables and Graphs OBJ: 3-1.1 To solve a linear system using a graph or a table NAT: CC A.CED.2| CC A.CED.3| CC A.REI.6| CC A.REI.11| A.4.d TOP: 3-1 Problem 1 Using a Graph or Table to Solve a System KEY: system of linear equations | graphing | solution of a system

3. ANS: B PTS: 1 DIF: L2 REF: 3-1 Solving Systems Using Tables and Graphs OBJ: 3-1.1 To solve a linear system using a graph or a table NAT: CC A.CED.2| CC A.CED.3| CC A.REI.6| CC A.REI.11| A.4.d TOP: 3-1 Problem 4 Classifying a System Without Graphing KEY: system of linear equations | independent system

4. ANS: C PTS: 1 DIF: L2 REF: 3-1 Solving Systems Using Tables and Graphs OBJ: 3-1.1 To solve a linear system using a graph or a table NAT: CC A.CED.2| CC A.CED.3| CC A.REI.6| CC A.REI.11| A.4.d TOP: 3-1 Problem 4 Classifying a System Without Graphing KEY: system of linear equations | dependent system

5. ANS: B PTS: 1 DIF: L2 REF: 3-2 Solving Systems AlgebraicallyOBJ: 3-2.1 To solve linear systems algebraically NAT: CC A.CED.2| CC A.CED.3| CC A.REI.5| CC A.REI.6| A.4.d TOP: 3-2 Problem 1 Solving by Substitution KEY: system of linear equations | substitution method

6. ANS: A PTS: 1 DIF: L2 REF: 3-2 Solving Systems AlgebraicallyOBJ: 3-2.1 To solve linear systems algebraically NAT: CC A.CED.2| CC A.CED.3| CC A.REI.5| CC A.REI.6| A.4.d TOP: 3-2 Problem 1 Solving by Substitution KEY: system of linear equations | substitution method

7. ANS: B PTS: 1 DIF: L2 REF: 3-2 Solving Systems AlgebraicallyOBJ: 3-2.1 To solve linear systems algebraically NAT: CC A.CED.2| CC A.CED.3| CC A.REI.5| CC A.REI.6| A.4.d TOP: 3-2 Problem 3 Solving by Elimination KEY: system of linear equations | solve by elimination

8. ANS: D PTS: 1 DIF: L2 REF: 3-2 Solving Systems AlgebraicallyOBJ: 3-2.1 To solve linear systems algebraically NAT: CC A.CED.2| CC A.CED.3| CC A.REI.5| CC A.REI.6| A.4.d TOP: 3-2 Problem 3 Solving by Elimination KEY: system of linear equations | solve by elimination

ID: A

2

9. ANS: D PTS: 1 DIF: L2 REF: 3-2 Solving Systems AlgebraicallyOBJ: 3-2.1 To solve linear systems algebraically NAT: CC A.CED.2| CC A.CED.3| CC A.REI.5| CC A.REI.6| A.4.d TOP: 3-2 Problem 5 Solving Systems Without Unique Solutions KEY: system of linear equations | solve by elimination | no solutions

10. ANS: D PTS: 1 DIF: L2 REF: 3-2 Solving Systems AlgebraicallyOBJ: 3-2.1 To solve linear systems algebraically NAT: CC A.CED.2| CC A.CED.3| CC A.REI.5| CC A.REI.6| A.4.d TOP: 3-2 Problem 5 Solving Systems Without Unique Solutions KEY: system of linear equations | solve by elimination | infinite solutions

11. ANS: A PTS: 1 DIF: L2 REF: 3-2 Solving Systems AlgebraicallyOBJ: 3-2.1 To solve linear systems algebraically NAT: CC A.CED.2| CC A.CED.3| CC A.REI.5| CC A.REI.6| A.4.d TOP: 3-2 Problem 2 Using Substitution to Solve a Problem KEY: substitution method | system of linear equations | word problem | problem solving

12. ANS: A PTS: 1 DIF: L3 REF: 3-2 Solving Systems AlgebraicallyOBJ: 3-2.1 To solve linear systems algebraically NAT: CC A.CED.2| CC A.CED.3| CC A.REI.5| CC A.REI.6| A.4.d TOP: 3-2 Problem 2 Using Substitution to Solve a Problem KEY: word problem | problem solving | system of linear equations | substitution method

13. ANS: D PTS: 1 DIF: L3 REF: 3-3 Systems of InequalitiesOBJ: 3-3.1 To solve systems of linear inequalities NAT: CC A.CED.3| CC A.REI.6| CC A.REI.12| A.4.d TOP: 3-3 Problem 2 Solving a System by Graphing KEY: system of inequalities | graphing

14. ANS: B PTS: 1 DIF: L3 REF: 3-3 Systems of InequalitiesOBJ: 3-3.1 To solve systems of linear inequalities NAT: CC A.CED.3| CC A.REI.6| CC A.REI.12| A.4.d TOP: 3-3 Problem 2 Solving a System by Graphing KEY: system of inequalities | graphing

15. ANS: A PTS: 1 DIF: L3 REF: 3-3 Systems of InequalitiesOBJ: 3-3.1 To solve systems of linear inequalities NAT: CC A.CED.3| CC A.REI.6| CC A.REI.12| A.4.d TOP: 3-3 Problem 2 Solving a System by Graphing KEY: system of inequalities | graphing

16. ANS: D PTS: 1 DIF: L2 REF: 3-3 Systems of InequalitiesOBJ: 3-3.1 To solve systems of linear inequalities NAT: CC A.CED.3| CC A.REI.6| CC A.REI.12| A.4.d TOP: 3-3 Problem 4 Solving a Linear/Absolute-Value Systems KEY: system of inequalities | graphing | absolute value

17. ANS: C PTS: 1 DIF: L3 REF: 3-3 Systems of InequalitiesOBJ: 3-3.1 To solve systems of linear inequalities NAT: CC A.CED.3| CC A.REI.6| CC A.REI.12| A.4.d TOP: 3-3 Problem 4 Solving a Linear/Absolute-Value Systems KEY: system of inequalities | graphing | absolute value

18. ANS: B PTS: 1 DIF: L2 REF: 3-3 Systems of InequalitiesOBJ: 3-3.1 To solve systems of linear inequalities NAT: CC A.CED.3| CC A.REI.6| CC A.REI.12| A.4.d TOP: 3-3 Problem 3 Using a System of Inequalities KEY: system of inequalities | graphing | problem solving | word problem

ID: A

3

19. ANS: C PTS: 1 DIF: L3 REF: 3-3 Systems of InequalitiesOBJ: 3-3.1 To solve systems of linear inequalities NAT: CC A.CED.3| CC A.REI.6| CC A.REI.12| A.4.d TOP: 3-3 Problem 3 Using a System of Inequalities KEY: system of inequalities | graphing | word problem | problem solving

20. ANS: A PTS: 1 DIF: L3 REF: 3-4 Linear ProgrammingOBJ: 3-4.1 To solve problems using linear programming NAT: CC A.CED.3| A.4.dTOP: 3-4 Problem 1 Testing Vertices KEY: linear programming | constraints | vertices | objective function | maximum value