Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Which linear system has the solution x = –2 and y =
6?
a. | x + 3y = 16
4x + 4y = 16 | c. | x +
2y = –2
2x + 4y = –4 | b. | x + 3y
= 17
2x + y = 15 | d. | 2x + y = –2
x + y =
16 |
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2.
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Which linear system has the solution x = 4 and y =
–2?
a. | x + 4y = 15
4x  = –17 | c. | 4x +
y = 14
–2x  = –16 | b. | 2x + 4y = 4
–2x
+ y = 14 | d. | x +
4y = 4
2x + 4y = 8 |
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3.
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Which graph represents the solution of the linear system: y =
–2 x  y + 6 = 2 x
    a. | Graph B | c. | Graph C | b. | Graph A | d. | Graph D |
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4.
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Which graph represents the solution of the linear system: –3 x
– y = –5 4 x – y =      a. | Graph A | c. | Graph C | b. | Graph B | d. | Graph D |
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5.
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Use the graph to approximate the solution of this linear system: 6 x
– 7 y = –4
–  y = 3 x + 7  a. | (–0.1, 3.8) | b. | (–2.1, –1.2) | c. | (–1.2, 3.8) | d. | (–2.1,
–0.1) |
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6.
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Match each situation to a linear system below. A. The perimeter of a rectangular
playground is 163 m. The length is 6 m less than double
the
width.
B. The perimeter of a rectangular playground is
163 m. The width is one-half the length
decreased by 6 m. C.
The perimeter of a rectangular playground is 163 m. The length
decreased by 6 m is double the
width.
i) 
ii) 
iii)  a. | A-i, B-ii, C-iii | c. | A-ii, B-i, C-iii | b. | A-iii, B-i, C-ii | d. | A-i, B-iii,
C-ii |
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7.
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Write a linear system to model this situation. Then verify which of the given
solutions is correct. A crate of 32 grapefruit has a total mass of 4.648 kg. When 9 grapefruit
are removed, the total mass is 3.622 kg. Verify the mass of the crate and the average mass of one
grapefruit. A.  B.  C.  D.  i)
The crate has a mass of 1 kg, and the mass of one grapefruit is
114 g. ii) The crate has a mass of 1.2 kg, and the
mass of one grapefruit is 114.2 g. iii) The crate has a mass
of 1 kg, and the mass of one grapefruit is 114.2 g. iv)
The crate has a mass of 1.2 kg, and the mass of one grapefruit is 57 g. a. | Part A-i | c. | Part B-iii | b. | Part C-ii | d. | Part D-iv |
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8.
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Use the graph to solve the linear system: y = –3 x –
5 y  = 3 x  a. | (1, –2) | c. | (1, 0) | b. | (–1, 0) | d. | (–1,
–2) |
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9.
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Which linear system is represented by this graph? a) 2x –
5y = –16
x =
1
b) 2x + 5y = 16
2x – 5y =
16
c) 2x – 5y = 16
x –  y =
–1
d) 2x + 5y = 16
x = –1
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a. | System a | b. | System d | c. | System b | d. | System
c |
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10.
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Determine the solution of the linear system represented by this graph. a) (2, 3.8)
b) (3.8, 2)
c)
(–3, 3.8)
d) (–2, 3.8) |  | | |
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Short Answer
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11.
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Quincy used this linear system to represent a situation involving a collection
of $5 bills and $10 bills:
f + t = 70
5f + 10t = 575
a)
What problem might Quincy have written?
b)
What does each variable represent?
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12.
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Solve this linear system by graphing. y = –8
–3 x + y = 7 
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13.
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a) Write a linear system to model this
situation: Angela is 24 years older than her cousin Zack. In 13
years, she will be double his age.
b) Use a graph to
solve this problem: How old are Angela and Zack now?
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14.
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Use graphing technology to solve this linear system.
Where necessary, write
the coordinates to the nearest tenth.
–3x – 5y = 12
–x
+ y = –10
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Problem
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15.
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These balance scales illustrate the two different sizes of cartons of detergent:
x represents the mass of a large carton and y represents the mass of a small
carton.   a)
Write a linear system to model the two balance scales. b) Use the diagrams of the balance
scales to verify that a large carton of detergent has a mass of 6 kg and a small carton has a mass of
3 kg.
c) Use the linear system to verify the masses of
the cartons in part b.
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16.
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a) Write a linear system whose solution
is: x = 5, y = –5.
b) Is there more than
one linear system with this solution? Explain.
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17.
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a) Use graphing technology to determine
the solution of this linear system. 17x + 10y =
9
7x – 6y = 29
b) Verify the
solution.
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