Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Identify two like terms and state how they are related.
–10x +
20y = 460
30x + 60y = 1620
a. | –10x and 30x; by a factor of –3 | c. | 30x and
60y; by a factor of 2 | b. | –10x and 20y; by a
factor of –2 | d. | –10x and 460; by a factor of  |
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2.
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3.
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4.
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For each equation, choose a divisor that is an integer. Then create an
equivalent linear system by dividing each term of the equation by the divisor.
12x –
8y = 1480
20x + 65y =
1370
a. | x – 3y = 370
x +
13y = 274 | c. | 3x – 2y = 370
4x +
13y = 274 | b. | 2x – 3y =
370
4x + 13y = 274 | d. | 3x – y =
370
4x + y = 274 |
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5.
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The first equation of a linear system is –6x + 12y =
–42. Choose a second equation to form a linear system with no solution.
i)
–6x + 12y = 126 ii) 18x –
36y = 126 iii) 18x + 12y =
126 iv) 18x + 36y = 0
a. | Equation iv | b. | Equation ii | c. | Equation iii | d. | Equation
i |
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6.
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Use substitution to solve this linear system.
x = 2y –
56
5x + 13y = 410
a. | (4, –30) | b. | (–4, 30) | c. | (4, 30) | d. | (–4,
–30) |
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7.
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Use substitution to solve this linear system. x = 4 + y x
+ 16 y = –264 a. | (–14, –14) | b. | (–10, –10) | c. | (–10,
–14) | d. | (–14, –10) |
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8.
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Use substitution to solve this problem:
Tanukah invested a total of $4350 in
two bonds. He invested in one bond at an annual interest rate of 6% and in another bond at an annual
interest rate of 8%. After one year, the total interest earned was $324.00. How much money did
Tanukah invest in each bond?
a. | $3150 at 6%,
$1200 at 8% | b. | $1200 at 6%,
$3150 at 8%
| c. | $3650 at 6%,
$700 at 8% | d. | $700 at 6%,
$3650 at 8%
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9.
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Use substitution to solve this problem:
Wai Sen scored 85% on part A of a
math test and 95% on part B of the math test. Her total mark for the test was 70. The total mark
possible for the test was 78.
How many marks is each part worth?
a. | Part A: 37 marks; part B: 37 marks | c. | Part A: 37 marks; part B: 41
marks | b. | Part A: 41 marks; part B: 41 marks | d. | Part A: 41 marks; part B: 37
marks |
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10.
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Use substitution to solve this linear system: x – y =
18  x +  y =  a. | x = 4; y = 18 | b. | x = –14; y =
–14 | c. | x = 4; y = –14 | d. | x = 4; y =
4 |
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11.
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Use an elimination strategy to solve this linear system.  
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12.
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Use an elimination strategy to solve this linear system.  
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13.
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Model this situation with a linear system:
Frieda has a 13% silver alloy and
a 31% silver alloy. Frieda wants to make 26 kg of an alloy that is 47% silver.
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14.
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Model this situation with a linear system:
At a campground, 5 large tanks and
5 small tanks contained 3200 L of drinking water. When one of the small tanks was replaced with a
large tank, there was 3400 L of drinking water.
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15.
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Use an elimination strategy to solve this linear system.  
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16.
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Which linear system is modelled by these balance scales? (Each small square on
the right side of the balance scales represents 2 kg.)  
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17.
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Model this situation with a linear system:
Nate borrowed $10 000 for his
university tuition. He borrowed part of the money at an annual interest rate of 2.4% and the rest of
the money at an annual interest rate of 4.5%. His total annual interest payment is $250.50.
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18.
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Determine the number of solutions of the linear system:
14x –
5y = 123
14x – 5y = 73
a. | no solution | c. | two solutions | b. | infinite solutions | d. | one solution |
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19.
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Determine the number of solutions for the linear system that models this
problem:
Find two numbers such that twice the first number is 3 greater than three times the
second number, and three times the first number is 22 greater than twice the second
number.
a. | two solutions | c. | no solution | b. | one solution | d. | infinite
solutions |
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20.
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For what value of k does the linear system below have infinite
solutions?  x + y = 14 kx + 2 y = 28 a. | 28 | b. |  | c. |  | d. | 0 |
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Short Answer
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21.
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Fill in the each blank below with the correct integer. System A
 -____:
 -____: | System B
7x + 6y = –376
–4x –
6y = 256 | | |
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22.
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Model this situation with a linear system:
A recycling depot pays 0.06¢
for a small can and 0.23¢ for a large can. Chara took 70 cans to the recycling depot and her
total refund was $22.35.
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23.
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Determine the number of solutions of this linear system.
7x –
3y = 43
7x – 3y = 13
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24.
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Determine the number of solutions of this linear system.
15x +
30y = –240
17x + 21y = 53
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25.
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Determine the number of solutions for the linear system that models this
problem:
Erica paid $6.00 for a bottle of water and 3 granola bars. Her friend paid $12.00 for
2 bottles of water and 6 granola bars. How much does a bottle of water cost?
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Problem
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26.
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a) Write a linear system to model the
situation: For the school play, the cost of one adult ticket is $6
and the cost of one student ticket is $4. Twice as many student tickets as adult tickets were sold.
The total receipts were $2016.
b) Use substitution to
solve the related problem: How many of each type of ticket were
sold?
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27.
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Use an elimination strategy to solve this linear
system. Verify the solution.
 
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28.
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Cashew nuts sell for $21.00/kg. Brazil nuts sell for $15.00/kg. A distributor
sold a total of 120 kg of cashew nuts and Brazil nuts for $2244. What mass of each type of nut was
sold?
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29.
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Use an elimination strategy to solve this linear
system. Verify the solution.
 
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30.
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Explain what happens when you try to solve this linear system using a
substitution strategy. What does this indicate about the graphs of these equations?  
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