Name: ________________________ Class: ___________________ Date: __________
Algebra 2 - Chapter 3 Review Solve the system by graphing. ____
3x 2y 7 1. 3x y 10 a.
c.
(3, –1) b.
(–1, 3) d.
(1, 3)
(3, 1)
1
ID: A
Name: ________________________
____
4x y 12 2. 4x 4y 8 a.
ID: A
c.
(–2, –4) b.
(–2, 4) d.
(4, –2)
(–4, –2)
Without graphing, is each system independent, dependent, or inconsistent? ____
____
x 5y 7 3. 4x y 7 a. inconsistent b. independent y 4x 6 4. 8x 2y 12 a. independent b. inconsistent
c.
dependent
c.
dependent
2
Name: ________________________
ID: A
Solve the system by substitution. ____
____
2x y 14 5. 3x y 11 a. (–4, –5) b. (5, 4)
c. d.
(–5, –4) (4, 5)
2.5x y 13.5 6. 2.25x y 12.25 a. (–5, 1) b. (–1, 5)
c. d.
(1, –5) (5, –1)
4x 4y 8 7. x 4y 7 a. (3, 5) b. (5, 3)
c. d.
(–3, –5) (–5, –3)
7x 8. 4x a. b.
c. d.
(–1, –2) (1, 2)
Solve the system using elimination. ____
____
2y 11 7y 10 (–2, –1) (2, 1)
What are the solutions of the following systems? ____
x 2y 10 9. 3x 6y 11 a. infinitely many solutions b. (–5, 2)
x 3y 9 ____ 10. x 3y 9 a. (5, –6) b. no solutions
c. d.
(5, –2) no solutions
c. d.
(–5, 6) infinitely many solutions
3
Name: ________________________
ID: A
____ 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. b.
a c a c
c 36 2a c 36
; 12 adults, 24 children ; 17 adults; 24 children
c. d.
a2
a a a a
c 36 c2 c 36
; 24 adults; 17 children ; 24 adults, 12 children
2c
____ 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. b.
length = 21.3 cm; width = 7.3 cm length = 21.3 cm; width = 14 cm
c. d.
4
length = 7.3 cm; width = 21.3 cm length = 7.9 cm; width = 14 cm
Name: ________________________
ID: A
Solve the system of inequalities by graphing.
y 3x 1 ____ 13. y 3x 2 a.
c.
b.
d.
5
Name: ________________________
x 2 ____ 14. y 1 a.
b.
ID: A
c.
d.
6
Name: ________________________
ID: A
y 3x 1 ____ 15. 1 y x 1 2 a.
c.
b.
d.
7
Name: ________________________
ID: A
Solve the system of inequalities by graphing.
y 4 ____ 16. y x 1 a.
c.
b.
d.
8
Name: ________________________
y x ____ 17. y 3x 2 5 a.
b.
ID: A
c.
d.
9
Name: ________________________
ID: A
____ 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
10
Name: ________________________
ID: A
____ 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.
b.
X Y X Y
X Y X Y
0 0
c.
Y 80 X 10
0 0
d.
Y 80 X 10
11
X Y X Y
X Y X Y
0 0 Y 80 X 10
0 0 Y 80 X 10
Name: ________________________
ID: A
What point in the feasible region maximizes the objective function?
____ 20. Constraints
x 0 y 0 x 5 y 1 y x 3 3
Objective function: C 4x 4y a. b.
(5,0) (1.5,3.5)
c. d.
12
(0,0) (0,3)
ID: A
Algebra 2 - Chapter 3 Review Answer Section 1. ANS: REF: OBJ: NAT: TOP: KEY: 2. ANS: REF: OBJ: NAT: TOP: KEY: 3. ANS: REF: OBJ: NAT: TOP: KEY: 4. ANS: REF: OBJ: NAT: TOP: KEY: 5. ANS: OBJ: NAT: TOP: KEY: 6. ANS: OBJ: NAT: TOP: KEY: 7. ANS: OBJ: NAT: TOP: KEY: 8. ANS: OBJ: NAT: TOP: KEY:
A PTS: 1 DIF: L2 3-1 Solving Systems Using Tables and Graphs 3-1.1 To solve a linear system using a graph or a table CC A.CED.2| CC A.CED.3| CC A.REI.6| CC A.REI.11| A.4.d 3-1 Problem 1 Using a Graph or Table to Solve a System system of linear equations | graphing | solution of a system A PTS: 1 DIF: L2 3-1 Solving Systems Using Tables and Graphs 3-1.1 To solve a linear system using a graph or a table CC A.CED.2| CC A.CED.3| CC A.REI.6| CC A.REI.11| A.4.d 3-1 Problem 1 Using a Graph or Table to Solve a System system of linear equations | graphing | solution of a system B PTS: 1 DIF: L2 3-1 Solving Systems Using Tables and Graphs 3-1.1 To solve a linear system using a graph or a table CC A.CED.2| CC A.CED.3| CC A.REI.6| CC A.REI.11| A.4.d 3-1 Problem 4 Classifying a System Without Graphing system of linear equations | independent system C PTS: 1 DIF: L2 3-1 Solving Systems Using Tables and Graphs 3-1.1 To solve a linear system using a graph or a table CC A.CED.2| CC A.CED.3| CC A.REI.6| CC A.REI.11| A.4.d 3-1 Problem 4 Classifying a System Without Graphing system of linear equations | dependent system B PTS: 1 DIF: L2 REF: 3-2.1 To solve linear systems algebraically CC A.CED.2| CC A.CED.3| CC A.REI.5| CC A.REI.6| A.4.d 3-2 Problem 1 Solving by Substitution system of linear equations | substitution method A PTS: 1 DIF: L2 REF: 3-2.1 To solve linear systems algebraically CC A.CED.2| CC A.CED.3| CC A.REI.5| CC A.REI.6| A.4.d 3-2 Problem 1 Solving by Substitution system of linear equations | substitution method B PTS: 1 DIF: L2 REF: 3-2.1 To solve linear systems algebraically CC A.CED.2| CC A.CED.3| CC A.REI.5| CC A.REI.6| A.4.d 3-2 Problem 3 Solving by Elimination system of linear equations | solve by elimination D PTS: 1 DIF: L2 REF: 3-2.1 To solve linear systems algebraically CC A.CED.2| CC A.CED.3| CC A.REI.5| CC A.REI.6| A.4.d 3-2 Problem 3 Solving by Elimination system of linear equations | solve by elimination 1
3-2 Solving Systems Algebraically
3-2 Solving Systems Algebraically
3-2 Solving Systems Algebraically
3-2 Solving Systems Algebraically
ID: A 9. ANS: OBJ: NAT: TOP: KEY: 10. ANS: OBJ: NAT: TOP: KEY: 11. ANS: OBJ: NAT: TOP: KEY: 12. ANS: OBJ: NAT: TOP: KEY: 13. ANS: OBJ: NAT: TOP: 14. ANS: OBJ: NAT: TOP: 15. ANS: OBJ: NAT: TOP: 16. ANS: OBJ: NAT: TOP: KEY: 17. ANS: OBJ: NAT: TOP: KEY: 18. ANS: OBJ: NAT: TOP: KEY:
D PTS: 1 DIF: L2 REF: 3-2 Solving Systems Algebraically 3-2.1 To solve linear systems algebraically CC A.CED.2| CC A.CED.3| CC A.REI.5| CC A.REI.6| A.4.d 3-2 Problem 5 Solving Systems Without Unique Solutions system of linear equations | solve by elimination | no solutions D PTS: 1 DIF: L2 REF: 3-2 Solving Systems Algebraically 3-2.1 To solve linear systems algebraically CC A.CED.2| CC A.CED.3| CC A.REI.5| CC A.REI.6| A.4.d 3-2 Problem 5 Solving Systems Without Unique Solutions system of linear equations | solve by elimination | infinite solutions A PTS: 1 DIF: L2 REF: 3-2 Solving Systems Algebraically 3-2.1 To solve linear systems algebraically CC A.CED.2| CC A.CED.3| CC A.REI.5| CC A.REI.6| A.4.d 3-2 Problem 2 Using Substitution to Solve a Problem substitution method | system of linear equations | word problem | problem solving A PTS: 1 DIF: L3 REF: 3-2 Solving Systems Algebraically 3-2.1 To solve linear systems algebraically CC A.CED.2| CC A.CED.3| CC A.REI.5| CC A.REI.6| A.4.d 3-2 Problem 2 Using Substitution to Solve a Problem word problem | problem solving | system of linear equations | substitution method D PTS: 1 DIF: L3 REF: 3-3 Systems of Inequalities 3-3.1 To solve systems of linear inequalities CC A.CED.3| CC A.REI.6| CC A.REI.12| A.4.d 3-3 Problem 2 Solving a System by Graphing KEY: system of inequalities | graphing B PTS: 1 DIF: L3 REF: 3-3 Systems of Inequalities 3-3.1 To solve systems of linear inequalities CC A.CED.3| CC A.REI.6| CC A.REI.12| A.4.d 3-3 Problem 2 Solving a System by Graphing KEY: system of inequalities | graphing A PTS: 1 DIF: L3 REF: 3-3 Systems of Inequalities 3-3.1 To solve systems of linear inequalities CC A.CED.3| CC A.REI.6| CC A.REI.12| A.4.d 3-3 Problem 2 Solving a System by Graphing KEY: system of inequalities | graphing D PTS: 1 DIF: L2 REF: 3-3 Systems of Inequalities 3-3.1 To solve systems of linear inequalities CC A.CED.3| CC A.REI.6| CC A.REI.12| A.4.d 3-3 Problem 4 Solving a Linear/Absolute-Value Systems system of inequalities | graphing | absolute value C PTS: 1 DIF: L3 REF: 3-3 Systems of Inequalities 3-3.1 To solve systems of linear inequalities CC A.CED.3| CC A.REI.6| CC A.REI.12| A.4.d 3-3 Problem 4 Solving a Linear/Absolute-Value Systems system of inequalities | graphing | absolute value B PTS: 1 DIF: L2 REF: 3-3 Systems of Inequalities 3-3.1 To solve systems of linear inequalities CC A.CED.3| CC A.REI.6| CC A.REI.12| A.4.d 3-3 Problem 3 Using a System of Inequalities system of inequalities | graphing | problem solving | word problem 2
ID: A 19. ANS: OBJ: NAT: TOP: KEY: 20. ANS: OBJ: TOP: KEY:
C PTS: 1 DIF: L3 REF: 3-3 Systems of Inequalities 3-3.1 To solve systems of linear inequalities CC A.CED.3| CC A.REI.6| CC A.REI.12| A.4.d 3-3 Problem 3 Using a System of Inequalities system of inequalities | graphing | word problem | problem solving A PTS: 1 DIF: L3 REF: 3-4 Linear Programming 3-4.1 To solve problems using linear programming NAT: CC A.CED.3| A.4.d 3-4 Problem 1 Testing Vertices linear programming | constraints | vertices | objective function | maximum value
3