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Alg 1 review for test chap 7
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Tom has a collection of 30 CDs and Nita has a collection of 12 CDs. Tom is adding 2 CDs a month to his
collection while Nita is adding 4 CDs a month to her collection. Write and graph a system to find the number
of months after which they will have the same number of CDs. Let x represent the number of months and y
the number of CDs.
a.
c.
y
y
50
50
(9, 48)
45
45
40
35
Number of CDs
Number of CDs
40
30
25
20
15
35
30
25
15
10
10
5
5
0
0
1
2
3
4
5
6
7
8
9
10
(3, 24)
20
0
x
0
1
2
Number of Months
9 months
4
5
6
7
8
9
10
x
3 months
b.
d.
y
50
50
45
45
40
40
35
Number of CDs
Number of CDs
y
(3, 35)
30
25
20
15
30
25
20
15
10
5
5
0
1
2
3
4
5
6
7
8
9
10
x
(9, 48)
35
10
0
0
0
1
Number of Months
3 months
____
3
Number of Months
2
3
4
5
6
7
8
9
10
x
Number of Months
48 months
2. Find a solution to the following system of equations. Use either elimination or substitution methods.
a. (2, 16)
b. (62, 16)
c. (0, 1)
d. (–2, 0)
____
3. Which graph represents the following system of equations?
y = 3x + 2
y = –x – 1
y
a.
c.
–4
–2
4
4
2
2
O
____
2
4
x
–2
O
–2
–4
–4
y
–2
–4
–2
b.
–4
y
4
2
2
2
4
x
4
x
2
4
x
y
d.
4
O
2
–4
–2
O
–2
–2
–4
–4
4. What is the solution of the system of equations? Substitution method is easiest in this case.
y = –3x + 6
y = –2x – 1
a. (7, –15)
b. (–5, 9)
c. (–1.4, 10.2)
d. (–15, 7)
Graph this system if necessary. Tell whether the system has no solution, one solution, or infinitely many
solutions.
____
5. y = –4x – 3
y = –4x + 2
a. no solutions
b. one solution
c. infinitely many solutions
Solve the system of equations using substitution.
____
6. y = 2x + 1
y = 3x + 4
a. (7, 3)
____
____
7. y = 4x – 8
y = 2x – 10
a. (5, 13)
b. (3, 13)
c. (3, 7)
d. (–3, –5)
b. (3, 4)
c. (3, –4)
d. (–1, –12)
8. The sum of two numbers is 68. Their difference is 28. Write a system of equations that describes this
situation. Solve by elimination to find the two numbers.
a. x + y = 68
c. x + y = 28
x – y = 28
y – x = 68
43 and 15
43 and 21
b. x + y = 68
d. x – y = 68
x – y = 28
x + y = 28
48 and 20
47 and 21
Solve the system using elimination.
____
9. 5x + y = 13
4x – y = 5
a. (1, 4)
____ 10. 4x + 2y = 6
2x + 6y = 28
a. (–1, 5)
b. (3, 2)
c. (2, 3)
d. (3, –2)
b. (5, –1)
c. (–1, 3)
d. (2, 4)
____ 11. A jar containing only nickels and dimes contains a total of 60 coins. The value of all the coins in the jar is
$4.45. Solve by elimination to find the number of nickels and dimes that are in the jar.
a. 30 nickels and 30 dimes
c. 29 nickels and 31 dimes
b. 31 nickels and 29 dimes
d. 28 nickels and 32 dimes
____ 12. By what number should you multiply the first equation to solve using elimination?
3x – 2y = –9
12x + 3y = –3
a. 4
b. 6
c. 3
d. 12
Graph the inequality.
____ 13.
y
a.
–4
–2
y
c.
4
4
2
2
O
2
4
x
–4
–2
O
–2
–2
–4
–4
2
4
x
y
b.
–4
____ 14.
–2
4
4
2
2
O
2
4
x
–4
–2
O
–2
–2
–4
–4
2
4
x
2
4
x
2
4
x
You need to rearrange the inequality before graphing it.
y
y
c.
a.
–4
–2
4
4
2
2
O
2
4
x
–2
–2
O
–2
–4
–4
y
–4
–4
–2
b.
____ 15.
y
d.
y
d.
4
4
2
2
O
2
4
x
–4
–2
O
–2
–2
–4
–4
y
a.
–4
–2
4
4
2
2
O
2
4
x
–2
O
–2
–4
–4
y
–2
–4
–2
b.
–4
y
c.
4
2
2
2
4
x
4
x
2
4
x
2
4
x
y
d.
4
O
2
–4
–2
O
–2
–2
–4
–4
____ 16.
y
a.
–4
–2
y
c.
4
4
2
2
O
2
4
x
–4
–2
O
–2
–2
–4
–4
y
b.
–4
4
4
2
2
O
–2
y
d.
2
x
4
–4
–2
O
–2
–2
–4
–4
2
Write the linear inequality shown in the graph.
____ 17.
y
4
2
–4
–2
O
2
4
x
–2
–4
a.
b.
____ 18.
c.
d.
c.
d.
y
4
2
–4
–2
O
2
4
x
–2
–4
a.
b.
4
x
____ 19. Find a solution of the linear inequality. You do not need to graph this equation to find the answer.
a. (3, 4)
b. (2, 1)
c. (3, 0)
d. (1, 1)
Solve the system of linear inequalities by graphing. The overlap of the shaded regions is shown in each
graph.
____ 20.
y
a.
–4
4
4
2
2
O
–2
2
4
x
–4
O
–2
–2
–2
–4
–4
y
b.
–4
y
c.
4
2
2
O
2
4
x
4
x
2
4
x
y
d.
4
–2
2
–4
O
–2
–2
–2
–4
–4
Short Answer
21. Graph the following linear inequalities on the same coordinate plane. What figure does the solution to all
three inequalities make?
Alg 1 review for test chap 7
Answer Section
MULTIPLE CHOICE
1. ANS: A
PTS: 1
DIF: L2
REF: 7-1 Solving Systems By Graphing
OBJ: 7-1.1 Solving Systems By Graphing
NAT: NAEP 2005 A4d | NAEP 2005 A4g | ADP J.3.3 | ADP J.4.3 | ADP J.5.2
STA: CO 9.2.3.b | CO 9.2.5.a
TOP: 7-1 Example 2
KEY: word problem | problem solving | system of linear equations | graphing a system of linear equations
2. ANS: D
PTS: 1
DIF: L3
REF: 7-1 Solving Systems By Graphing
OBJ: 7-1.1 Solving Systems By Graphing
NAT: NAEP 2005 A4d | NAEP 2005 A4g | ADP J.3.3 | ADP J.4.3 | ADP J.5.2
STA: CO 9.2.3.b | CO 9.2.5.a
TOP: 7-1 Example 1
KEY: system of linear equations | graphing a system of linear equations
3. ANS: D
PTS: 1
DIF: L2
REF: 7-1 Solving Systems By Graphing
OBJ: 7-1.1 Solving Systems By Graphing
NAT: NAEP 2005 A4d | NAEP 2005 A4g | ADP J.3.3 | ADP J.4.3 | ADP J.5.2
STA: CO 9.2.3.b | CO 9.2.5.a
TOP: 7-1 Example 1
KEY: system of linear equations | graphing a system of linear equations
4. ANS: A
PTS: 1
DIF: L2
REF: 7-1 Solving Systems By Graphing
OBJ: 7-1.1 Solving Systems By Graphing
NAT: NAEP 2005 A4d | NAEP 2005 A4g | ADP J.3.3 | ADP J.4.3 | ADP J.5.2
STA: CO 9.2.3.b | CO 9.2.5.a
TOP: 7-1 Example 1
KEY: system of linear equations | graphing a system of linear equations
5. ANS: A
PTS: 1
DIF: L2
REF: 7-1 Solving Systems By Graphing
OBJ: 7-1.2 Analyzing Special Types of Systems
NAT: NAEP 2005 A4d | NAEP 2005 A4g | ADP J.3.3 | ADP J.4.3 | ADP J.5.2
STA: CO 9.2.3.b | CO 9.2.5.a
TOP: 7-1 Example 4 | 7-1 Example 5
KEY: system of linear equations | graphing a system of linear equations | no solution | infinitely many
solutions
6. ANS: D
PTS: 1
DIF: L2
REF: 7-2 Solving Systems Using Substitution
OBJ: 7-2.1 Using Substitution
NAT: NAEP 2005 A4g | ADP J.3.3 | ADP J.5.2
STA: CO 9.2.3.b
TOP: 7-2 Example 1
KEY: system of linear equations | substitution method
7. ANS: D
PTS: 1
DIF: L2
REF: 7-2 Solving Systems Using Substitution
OBJ: 7-2.1 Using Substitution
NAT: NAEP 2005 A4g | ADP J.3.3 | ADP J.5.2
STA: CO 9.2.3.b
TOP: 7-2 Example 1
KEY: system of linear equations | substitution method
8. ANS: B
PTS: 1
DIF: L3
REF: 7-3 Solving Systems Using Elimination
OBJ: 7-3.1 Adding or Subtracting to Solve Systems
NAT: NAEP 2005 A4g | ADP J.3.3 | ADP J.5.2
STA: CO 9.2.3.b
KEY: word problem | problem solving | system of linear equations | elimination method | adding or
subtracting equations
9. ANS: C
PTS: 1
DIF: L2
REF: 7-3 Solving Systems Using Elimination
OBJ: 7-3.1 Adding or Subtracting to Solve Systems
NAT: NAEP 2005 A4g | ADP J.3.3 | ADP J.5.2
STA: CO 9.2.3.b
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
TOP: 7-3 Example 1
KEY: system of linear equations | elimination method | adding or subtracting equations
ANS: A
PTS: 1
DIF: L2
REF: 7-3 Solving Systems Using Elimination
OBJ: 7-3.2 Multiplying First to Solve Systems
NAT: NAEP 2005 A4g | ADP J.3.3 | ADP J.5.2
STA: CO 9.2.3.b
TOP: 7-3 Example 3
KEY: system of linear equations | elimination method | adding or subtracting equations
ANS: B
PTS: 1
DIF: L2
REF: 7-3 Solving Systems Using Elimination
OBJ: 7-3.2 Multiplying First to Solve Systems
NAT: NAEP 2005 A4g | ADP J.3.3 | ADP J.5.2
STA: CO 9.2.3.b
TOP: 7-3 Example 4
KEY: word problem | problem solving | system of linear equations | elimination method | adding or
subtracting equations
ANS: A
PTS: 1
DIF: L2
REF: 7-3 Solving Systems Using Elimination
OBJ: 7-3.2 Multiplying First to Solve Systems
NAT: NAEP 2005 A4g | ADP J.3.3 | ADP J.5.2
STA: CO 9.2.3.b
TOP: 7-3 Example 3
KEY: system of linear equations | elimination method | adding or subtracting equations
ANS: B
PTS: 1
DIF: L2
REF: 7-5 Linear Inequalities
OBJ: 7-5.1 Graphing Linear Inequalities NAT: NAEP 2005 A3a | ADP J.4.4
STA: CO 9.2.5.a
TOP: 7-5 Example 1
KEY: linear inequality | graphing
ANS: A
PTS: 1
DIF: L3
REF: 7-5 Linear Inequalities
OBJ: 7-5.1 Graphing Linear Inequalities NAT: NAEP 2005 A3a | ADP J.4.4
STA: CO 9.2.5.a
TOP: 7-5 Example 2
KEY: linear inequality | graphing
ANS: C
PTS: 1
DIF: L2
REF: 7-5 Linear Inequalities
OBJ: 7-5.1 Graphing Linear Inequalities NAT: NAEP 2005 A3a | ADP J.4.4
STA: CO 9.2.5.a
TOP: 7-5 Example 1
KEY: linear inequality | graphing
ANS: B
PTS: 1
DIF: L2
REF: 7-5 Linear Inequalities
OBJ: 7-5.1 Graphing Linear Inequalities NAT: NAEP 2005 A3a | ADP J.4.4
STA: CO 9.2.5.a
TOP: 7-5 Example 1
KEY: linear inequality | graphing
ANS: D
PTS: 1
DIF: L2
REF: 7-5 Linear Inequalities
OBJ: 7-5.1 Graphing Linear Inequalities NAT: NAEP 2005 A3a | ADP J.4.4
STA: CO 9.2.5.a
TOP: 7-5 Example 1
KEY: linear inequality | graphing
ANS: A
PTS: 1
DIF: L2
REF: 7-5 Linear Inequalities
OBJ: 7-5.1 Graphing Linear Inequalities NAT: NAEP 2005 A3a | ADP J.4.4
STA: CO 9.2.5.a
TOP: 7-5 Example 1
KEY: linear inequality | graphing
ANS: D
PTS: 1
DIF: L2
REF: 7-5 Linear Inequalities
OBJ: 7-5.1 Graphing Linear Inequalities NAT: NAEP 2005 A3a | ADP J.4.4
STA: CO 9.2.5.a
TOP: 7-5 Example 1
KEY: linear inequality | graphing
ANS: B
PTS: 1
DIF: L2
REF: 7-6 Systems of Linear Inequalities
OBJ: 7-6.1 Solving Systems of Linear Inequalities by Graphing
NAT: NAEP 2005 A4g | ADP J.4.4
STA: CO 9.2.5.a
TOP: 7-6 Example 1
KEY: linear inequality | graphing | system of linear inequalities | graphing a system of linear inequalities
SHORT ANSWER
21. ANS:
y
6
4
2
–4
–2
O
2
4
x
–2
–4
–6
The figure is an isosceles triangle.
PTS: 1
DIF: L4
REF: 7-5 Linear Inequalities
OBJ: 7-5.1 Graphing Linear Inequalities NAT: NAEP 2005 A3a | ADP J.4.4
STA: CO 9.2.5.a
KEY: linear inequality | graphing