Question 1
What is the value of the y variable in the solution to the following system of equations?
2x + y = 5
x + 3y = 0
−1
1
3
−3
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Question 2
For the following system, if you isolated y in the second equation to use the Substitution Method, what expression would you substitute into the first equation?
2x + y = 2
x − y = −6
−6 − x
−6 + x
6 − x
6 + x
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Question 3
Terry solved the system of equations below. What mistake did he make in his work?
3x + y = 6
x − 2y = 2
y = 6 − 3x
x − 2(6 − 3x) = 2
x − 12 − 6x = 2
−5x − 12 = 2
+12 +12
x = −2.8
3(−2.8) + y = 6
−8.4 + y = 6
+8.4 +8.4
y = 14.4
He should have substituted 6 + 3x.
He combined like terms incorrectly. It should have been 5x instead of −5x.
He made a mistake in distributing −2.
He made no mistake.
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Question 4
Auditions for a new, upcoming band in Chicago were held with 102 men and women trying out for the lead singer position. If twice the number of men less three times the number of women is equal to −6, how many women auditioned?
38
40
42
60
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Question 5
Solve the following system.
y = x + 3
4x + y = 18
(6, 3)
(3, 6)
(−3, 6)
(3, −6)
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Question 6
The graph of the following system of equations is
2x + y = 6
6x + 3y = 12
Overlapping lines
Parallel lines
Intersecting lines
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Question 7
There were 190 people at the Junior-Senior dance Sasha and her friends attended. Junior tickets were $2.00 each and Senior tickets were $3.50 each. The total receipts for the dance were $530. How many Juniors bought tickets?
70
80
90
100
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Question 8
Two cars leave town going in opposite directions. One car is traveling 70 miles per hour (mph), and the other car is traveling 50 mph. How long will it take before the cars are 240 miles apart?
4 hrs
6 hrs
2 hrs
5 hrs
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Question 9
If you wanted to eliminate the y variable by adding the two equations in the following system, what could be your first step?
3x + y = 6
4x − 5y = 10
Multiply the first equation by 5.
Multiply the first equation by −5.
Multiply the first equation by −4.
Add the two equations together.
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Question 10
Solve the following system.
x − y = 10
x + y = 8
(−9, 1)
(9, −1)
(9, 1)
(−1, 9)
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Question 11
Which equation would you use to solve the following word problem?
Sasha's mom decided to get her a cell phone for her birthday. Cell Plus has a plan that costs $23.95 per month plus an additional $0.05 per minute. Cell Best has a plan that costs $28.95 per month plus an additional $0.03 per minute. How many minutes can Sasha talk and have the same cost each month?
0.08m = 5.00
23.95 + 0.05m = 28.98
28.95 + 0.03m = 24.00
23.95 + 0.05m = 28.95 + 0.03m
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Question 12
The graph below is represented by which system of inequalities?
x + y > 1 and 2x + y > 4
x + y < 1 and 2x + y > 4
x + y < 1 and 2x + y < 4
x + y > 1 and 2x + y < 4
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Question 13
Choose the graph that matches the following system of equations.
5x + 2y = 2
3x – 3y = 18
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Question 14
Your piggy bank has a total of 47 coins in it; some are dimes and some are nickels. If you have a total of $3.95, how many nickels do you have?
Numerical Answers Expected!
Answer for Blank 1:
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Question 15
The graph of a system of equations will intersect at exactly 2 points.
Always
Sometimes
Never
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Question 16
Which point lies in the solution set for the following system of inequalities?
2x + y > 8
x − y < 2
(1, 1)
(3, 4)
(5, −2)
(6, 1)
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Question 17 (Multiple Choice Worth 4 points)
Carroll High School has a total of 94 boys and girls who play sports. If the number of boys is 9 more than four times the number of girls, how many boys play sports at this high school?
17
23
77
92
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Question 18
Select the system of equations that corresponds to the given graph.
4x + 2y = 12
4x + 2y = 4
2x + 3y = 4
6x + 9y = 12
2x + 4y = 12
2x + y = 3
2x + 3y = 8
−x + y = −4
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Question 19
Which set of equations would be used to solve this word problem?
An airplane flew 5 hours with a 50 mph head wind. The return trip with a tail wind of the same speed took 3 hours. Find the speed of the plane in still air.
d = 8(r + 50)
d = 5(r + 50) and d = 3(r − 50)
d = 5(r − 50) and d = 3(r + 50)
None of these systems can be used to solve this problem.
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Question 20
Part 1:
For the following system of equations, write your own real world scenario that describes what is happening. Use complete sentences and correct grammar in your scenario.
Part 2:
Solve the system and explain what the results mean according to your scenario.
2x + y = 10
3x + 4y = 25
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Question 21
You graph a system of equations and the two lines overlap, or lie right on top of one another. Explain what this tells you about the:
solution to the system
the two equations
the result if the system was solved algebraically