Name: _____________________________________ Period: __________ Date: ______________
ID: A
Algebra 2 Chapter 3 Practice TEST Show all work for full credit!
9. Solve the system of inequalities by graphing.
ÏÔ
ÔÔ y ≤ −2x + 1
ÌÔ
ÔÓÔ y > 2x − 1
1. Solve the system of equations using any method.
ÏÔ
ÔÔ −3x + 2y = 2
ÌÔ
ÔÓÔ 5x − 2y = 2
2. Use elimination to solve the system.
ÏÔ
ÔÔÔ −7x + 4y = −12
.
ÌÔÔ
ÔÔ 5x − 4y = 12
Ó
10. Solve the system of inequalities by graphing.
ÏÔ
Ôy ≥ x
ÌÔ
ÔÓÔ y > |3x − 2| − 5
11. Solve the system of equations using any method.
ÔÏÔ −x + y + z = −3
ÔÔ
Ô
z = 2
ÌÔ
ÔÔ
ÔÔ −3x + 3y + 2z = −11
Ó
3. Solve the system using either method of
substitution or elimination.
ÔÏ 3x + 5y + 4z = 13
ÔÔ
ÔÔ
ÔÌÔ 5x + 2y + 3z = −9
ÔÔ
ÔÓ 6x + 3y + 4z = −8
12. Solve the system by graphing.
ÔÏ −4x − 4y + 4 = 0
Ô
ÌÔ
ÔÔÓ −8x − 8y = 0
ÔÏÔ 3x − 2y = 14
4. Classify the system ÔÌ
, and determine
ÔÔÔ 8y − 12x = −56
Ó
the number of solutions.
13. Solve the system of inequalities by graphing.
ÔÏÔ y ≥ −3x − 1
ÔÔ
Ô
1
ÔÌÔ
ÔÔ y ≤ x + 3
ÔÓ
2
5. Without graphing, classify each system as
independent, dependent, or inconsistent.
ÏÔ
Ô y = −6x − 3
ÌÔ
ÔÓÔ −6x − y = 3
14. Solve the system of inequalities by graphing.
ÔÏÔ x ≥ −2
Ô
ÔÌÔ
ÔÓ y > 0
6. Without graphing, classify each system as
independent, dependent, or inconsistent.
ÏÔ
ÔÔ −3x + 3y = −9
ÌÔ
ÔÔÓ y = x − 1
15. Which of the following points lies in the plane
represented by 5x + 2y + 3z = 5?
a. (5, 6, –8)
b. (1, –5, 2)
c. (–4, 3, 3)
d. (10, –9, –9)
7. Describe the location of the point in coordinate
space.
(10, 8, 3)
16. Plot the points (–3, –4, 2) and (2, 3, –2 ) in a
three-dimensional coordinate system.
8. Use substitution to solve the system
ÔÏÔ 3x + y = 5
Ô
.
ÔÌÔ
ÔÓ y = x − 3
17. Graph x + y + z = 3 .
1
ID: A
18. Solve the system by graphing.
ÏÔ
Ô −3x − y = −10
ÌÔ
ÔÓÔ 4x − 4y = 8
28. Without graphing, classify each system as
independent, dependent, or inconsistent.
ÏÔ
Ô −2x − y = 9
ÌÔ
ÔÓÔ 3x − 4y = −8
19. Solve the system by the method of substitution.
ÔÏÔ x + y + 3z = −4
ÔÔ
Ô
ÌÔ −x − y − 2z = 5
ÔÔ
ÔÔ 2x − z = −3
Ó
29. Solve the system by any method.
ÔÏ 1
ÔÔ
ÔÔ v + w = 10
Ô2
ÌÔ
ÔÔ 2
ÔÔ v + 4w = 8
ÔÓ 3
20. Use the elimination method to solve the system.
ÔÏ 5x + 3y = −6
Ô
ÌÔ
ÔÔÓ 3x − 2y = 4
30. A group of 52 people attended a ball game. There
were three times 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 children who were in the group.
ÏÔ
Ô a + c = 52
a. ÌÔ
; 39 adults; 25 children
ÔÓÔ a = c + 3
ÏÔ
Ô a + c = 52
; 39 adults, 13 children
b. ÔÌÔ
ÔÔÓ a = 3c
ÏÔ
Ô a + c = 52
; 25 adults; 39 children
c. ÔÌÔ
ÔÔÓ c = a + 3
ÏÔ
Ô a + c = 52
; 13 adults, 39 children
d. ÔÌÔ
ÔÔÓ c = 3a
21. Use the elimination method to solve the system.
ÔÏÔ −x + 2y = 10
Ô
ÔÌÔ
ÔÓ −3x + 6y = 11
22. Solve the system of inequalities by graphing.
ÏÔ
ÔÔ y ≥ 4
ÌÔ
ÔÓÔ y > |2x + 4|
23. Equivalent systems of two linear equations ____
have the same solutions.
a. always
b. sometimes
c. never
24. Graph 9x + 18y − 12z = 36.
25. Use the elimination method to solve the system.
ÏÔ
ÔÔ 0.18f − 0.3g = 3
ÌÔ
ÔÓÔ 0.15g − 0.9f = −5.55
26. Use the any method to solve the system.
ÏÔ
ÔÔ 2x − 2y + z = −15
ÔÔ
ÌÔ 6x − 3y − z = −19
ÔÔ
ÔÔ 3x − y − z = −6
Ó
ÏÔ
Ô y < −3x + 2
27. Graph the system of inequalities ÔÌÔ
.
ÔÔÓ y ≥ 4x − 1
2
ID: A
Algebra 2 Chapter 3 Practice TEST Show all work for full credit!
Answer Section
1. ANS:
(2, 4)
KEY: system of linear equations | solve by elimination
2. ANS:
(0, –3)
KEY: linear equations | systems of equations | solving | elimination
3. ANS:
(–3, 6, –2)
KEY: system with three variables | substitution method | solve by elimination
4. ANS:
The system is consistent and dependent and has infinitely many solutions.
KEY: classifying | linear systems | consistent | inconsistent | dependent | independent
5. ANS:
dependent
KEY: system of linear equations | dependent system
6. ANS:
inconsistent
KEY: system of linear equations | inconsistent system
7. ANS:
From the origin, move 10 units forward, 8 units right, and 3 units up.
KEY: three dimensions
8. ANS:
(2, −1)
KEY: substitution method | systems of equations | linear systems
1
ID: A
9. ANS:
KEY: system of inequalities | graphing
10. ANS:
KEY: system of inequalities | graphing | absolute value
11. ANS:
(8, 3, 2)
KEY: system with three variables | substitution method
2
ID: A
12. ANS:
no solutions
KEY: system of linear equations | graphing | inconsistent system
13. ANS:
KEY: system of inequalities | graphing
3
ID: A
14. ANS:
KEY: system of inequalities | graphing
15. ANS: D
KEY: graphing | three dimensions
16. ANS:
KEY: three dimensions | graphing
17. ANS:
KEY: graphing | three dimensions
4
ID: A
18. ANS:
(3, 1)
KEY: system of linear equations | graphing
19. ANS:
(–1, –6, 1)
KEY: system with three variables | substitution method
20. ANS:
(0, –2)
KEY: system of linear equations | solve by elimination | equivalent systems
21. ANS:
no solutions
KEY: system of linear equations | solve by elimination | no solutions
22. ANS:
KEY: system of inequalities | graphing | absolute value
23. ANS: A
KEY: system of linear equations | equivalent systems | reasoning | always sometimes never
5
ID: A
24. ANS:
KEY: graphing | three dimensions
25. ANS:
f = 5, g = –7
KEY: system of linear equations | solve by elimination
26. ANS:
(–3, 2, –5)
KEY: system with three variables | solve by elimination
27. ANS:
KEY: systems of linear inequalities | graphing systems of inequalities
28. ANS:
independent
KEY: system of linear equations | independent system
29. ANS:
(24, –2)
KEY: substitution method | system of linear equations
30. ANS: D
KEY: substitution method | system of linear equations | word problem | problem solving
6