Name: ________________________ Class: ___________________ Date: __________
Systems Test Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
____
1. What is the solution of the system of equations?
y = 3x + 7
y=x–9
a. (–1, –10)
b. (–17, –8)
c.
(4, 19)
d.
(–8, –17)
2. Find the value of b that makes the system of equations have the solution (3, 5).
y = 3x – 4
y = bx + 2
a. 0
b. –1
c. 2
d. 1
Tell whether the system has no solution, one solution, or infinitely many solutions.
____
3. y = 5x – 4
y = 5x – 5
a. no solutions
b. one solution
c. infinitely many solutions
____
4. y = x + 4
y–4=x
a. infinitely many solutions
b. no solutions
c. one solution
Solve the system of equations using any method.
____
5. y = x + 6
y = –2x – 3
b.
(–3, 3)
c.
ÁÊÁ
˜ˆ
ÁÁ −6, 3 ˜˜˜
Á
2 ˜¯
Ë
d.
(4, –11)
1
6. 3y = – x + 2
2
y = –x + 9
a. (3, 6)
b.
(20, –4)
c.
(10, –1)
d.
(–1, 8)
7. y = 4x + 6
y = 2x
a. (–3, –6)
b.
(3, 6)
c.
(6, 3)
d.
(1, 2)
a.
____
____
(1, 7)
1
ID: A
Name: ________________________
____
8. 3x + 2y = 7
y = –3x + 11
a.
____
ID: A
(6, –3)
b.
(6, –7)
c.
ÊÁ
ˆ
ÁÁ −4, 19 ˜˜˜
ÁÁ
2 ˜˜¯
Ë
d.
(5, –4)
9. The sum of two numbers is 82. Their difference is 24. Write a system of equations that describes this
situation. Solve by elimination to find the two numbers.
a. x + y = 82
c. x + y = 24
x – y = 24
y – x = 82
48 and 24
48 and 30
b. x – y = 82
d. x + y = 82
x + y = 24
x – y = 24
52 and 30
53 and 29
Solve the system using any method.
____ 10. 3x + 3y = –9
3x – 3y = 21
a. (3, –6)
b.
(–5, 2)
c.
(3, 3)
d.
(2, –5)
____ 11. x + 2y = –6
3x + 8y = –20
a. (–1, –4)
b.
(–4, 4)
c.
(–4, –1)
d.
(3, 1)
____ 12. 5x = –25 + 5y
10y = 42 + 2x
a. (–1, 2)
b.
(–1, 4)
c.
(4, –1)
d.
(5, 10)
____ 13. By what number should you multiply the first equation to solve using elimination?
–3x – 2y = 2
–9x + 3y = 24
a. 6
b. –9
c. –3
d. 3
Essay
14. A motorboat can go 16 miles downstream on a river in 20 minutes. It takes 30 minutes for this boat to go
back upstream the same 16 miles.
Let x = the speed of the boat.
Let y = the speed of the current.
Write an equation for the motion of the motorboat downstream.
a.
Write an equation for the motion of the motorboat upstream.
b.
Find the speed of the current.
c.
2
Name: ________________________
ID: A
15. Niki has 8 coins worth $1.40. Some of the coins are nickels and some are quarters.
Let q = the number of quarters and n = the number of nickels. Write an equation
a.
relating the number of quarters and nickels to the total number of coins.
Write an equation relating the value of the quarters and the value of the nickels to the
b.
total value of the coins.
How many of each coin does Niki have?
c.
3
ID: A
Systems Test Review
Answer Section
MULTIPLE CHOICE
1. 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: NJ 4.3.12 B.2g | 8NJ 4.5.E.2 | 8NJ 4.5.C.2 | 8NJ 4.5.D.4 | NJ 4.2.12 C.1c
TOP: 7-1 Example 1
KEY: 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: NJ 4.3.12 B.2g | 8NJ 4.5.E.2 | 8NJ 4.5.C.2 | 8NJ 4.5.D.4 | NJ 4.2.12 C.1c
KEY: system of linear equations | graphing a system of linear equations
3. 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: NJ 4.3.12 B.2g | 8NJ 4.5.E.2 | 8NJ 4.5.C.2 | 8NJ 4.5.D.4 | NJ 4.2.12 C.1c
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
4. 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: NJ 4.3.12 B.2g | 8NJ 4.5.E.2 | 8NJ 4.5.C.2 | 8NJ 4.5.D.4 | NJ 4.2.12 C.1c
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
5. ANS: B
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: NJ 4.3.12 D.2a | 8NJ 4.5.E.3 | NJ 4.3.12 D.1a | NJ 4.3.12 D.1b
TOP: 7-2 Example 1
KEY: system of linear equations | substitution method
6. ANS: C
PTS: 1
DIF: L3
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: NJ 4.3.12 D.2a | 8NJ 4.5.E.3 | NJ 4.3.12 D.1a | NJ 4.3.12 D.1b
TOP: 7-2 Example 2
KEY: system of linear equations | substitution method
7. ANS: A
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: NJ 4.3.12 D.2a | 8NJ 4.5.E.3 | NJ 4.3.12 D.1a | NJ 4.3.12 D.1b
TOP: 7-2 Example 1
KEY: system of linear equations | substitution method
1
ID: A
8. ANS: D
PTS: 1
DIF: L3
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: NJ 4.3.12 D.2a | 8NJ 4.5.E.3 | NJ 4.3.12 D.1a | NJ 4.3.12 D.1b
TOP: 7-2 Example 2
KEY: system of linear equations | substitution method
9. ANS: D
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: NJ 4.3.12 D.2a | 8NJ 4.5.E.3 | NJ 4.3.12 D.1a | NJ 4.3.12 D.1b
KEY: word problem | problem solving | system of linear equations | elimination method | adding or
subtracting equations
10. ANS: D
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: NJ 4.3.12 D.2a | 8NJ 4.5.E.3 | NJ 4.3.12 D.1a | NJ 4.3.12 D.1b
TOP: 7-3 Example 1
KEY: system of linear equations | elimination method | adding or subtracting equations
11. ANS: C
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: NJ 4.3.12 D.2a | 8NJ 4.5.E.3 | NJ 4.3.12 D.1a | NJ 4.3.12 D.1b
TOP: 7-3 Example 3
KEY: system of linear equations | elimination method | adding or subtracting equations
12. ANS: B
PTS: 1
DIF: L3
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: NJ 4.3.12 D.2a | 8NJ 4.5.E.3 | NJ 4.3.12 D.1a | NJ 4.3.12 D.1b
TOP: 7-3 Example 3
KEY: system of linear equations | elimination method | adding or subtracting equations
13. ANS: D
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: NJ 4.3.12 D.2a | 8NJ 4.5.E.3 | NJ 4.3.12 D.1a | NJ 4.3.12 D.1b
TOP: 7-3 Example 3
KEY: system of linear equations | elimination method | adding or subtracting equations
2
ID: A
ESSAY
14. ANS:
[4] a.
b.
[3]
[2]
[1]
(x + y)
(x − y)
1
3
1
2
= 16
= 16
8 mph
c.
minor computation error
misapplication of rt = d formula
correct answer, but no equations shown
PTS: 1
DIF: L3
REF: 7-4 Applications of Linear Systems
OBJ: 7-4.1 Writing Systems of Linear Equations
NAT: NAEP 2005 A4g | ADP J.3.3 | ADP J.4.3 | ADP J.5.2
STA: NJ 4.3.12 D.2a | 8NJ 4.5.E.3 | NJ 4.3.12 C.1a
KEY: extended response | rubric-based question | word problem | problem solving | system of linear
equations | graphing a system of linear equations | substitution method | elimination method | motion problem
15. ANS:
n+q = 8
[4]
a.
5n + 25q = 140
b.
5 quarters and 3 nickels
c.
[3]
minor computation error
[2]
(a) and (b) correct
[1]
correct answer, but no equations shown
PTS: 1
DIF: L3
REF: 7-4 Applications of Linear Systems
OBJ: 7-4.1 Writing Systems of Linear Equations
NAT: NAEP 2005 A4g | ADP J.3.3 | ADP J.4.3 | ADP J.5.2
STA: NJ 4.3.12 D.2a | 8NJ 4.5.E.3 | NJ 4.3.12 C.1a
KEY: extended response | rubric-based question | word problem | problem solving | system of linear
equations | graphing a system of linear equations | substitution method | elimination method
3