Name: ________________________ Class: ___________________ Date: __________
ID: A
Systems Review 2014
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Find the best algebraic method to solve the given system by inspecting the equations.
2x - 4y = -2
-6x + 4y = 14
a. subtraction b. addition c. substitution d. multiplication
Hydrology: (Problems 2 and 3)
Scientists observe the depth of two lakes for three months. The initial depth of the lakes and the rate of
change in depth of each lake are shown in the table.
Let d represent the initial depth of a lake and t represent the number of weeks.
____
2. Which system of equations could you use to compare the depths of the lakes over that time period?
a.
____
d = –58
d = 3t – 53
b.
d = 58t
d = 53t
c.
d = 58
d = 53 + 3t
d.
d=0
d = 3t
3. Which lake is deeper after 5 weeks?
a. Lake 1 is deeper. b. Lake 2 is deeper. c. The lakes have the same depth.
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Name: ________________________
ID: A
What is the solution of the system? Use a graph.
____
4. y = 2x + 1
y = –3x – 1
a.
c.
b.
d.
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Name: ________________________
____
____
ID: A
5. y = x + 5
y = –5x – 1
a.
b.
c.
d.
6. Tom has a collection of 30 CDs and Nita has a collection of 18 CDs. Tom is adding 1 CD a month to his
collection while Nita is adding 5 CDs a month to her collection. Find the number of months after which they
will have the same number of CDs.
a. 33 months b. 1 month c. 2 months d. 3 months
3
Name: ________________________
ID: A
What is the solution of the system? Use a graph.
____
7. y = –3x + 2
y = –3x + 4
a.
c.
infinitely many solutions
no solutions
d.
b.
(0, 2)
(0, 4)
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Name: ________________________
____
ID: A
8. y = –5x – 2
y + 2 = –5x
a.
c.
infinitely many solutions
(0, –2)
d.
b.
no solutions
(0, 2)
What is the solution of the system? Use substitution.
____
9. y = x + 6
y = 2x
a. (6, 12) b. (2, 4) c. (–12, –6) d. (–6, –12)
____ 10. x = –2y + 10
–6y = 6x – 6
z = –3x + 10y
a. x = 114, y = 9, z = –8 b. x = –8, y = 114, z = 9 c. x = –8, y = 9, z = 114 d. x = 9, y = –8, z = 114
What is the solution of the system? Use substitution.
____ 11. 8x − 2y = 10
3x − y = 9
a. (2, 3) b. (2, –3) c. (–2, –12) d. (–4, –21)
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Name: ________________________
ID: A
____ 12. A corner store sells two kinds of baked goods: cakes and pies. A cake costs $5 and a pie costs $7. In one day,
the store sold 15 baked goods for a total of $91. How many cakes did they sell?
a. 5 cakes b. 7 cakes c. 8 cakes d. 4 cakes
How many solutions does the system have?
____ 13. x = −4y + 4
2x + 8y = 8
a. one solution b. two solutions c. infinitely many solutions d. no solution
What is the solution of the system? Use elimination.
____ 14. 5x + 4y = –2
x – 4y = 14
a. (4, 1) b. (–3, 2) c. (2, –3) d. (3, –4.3)
What is the solution of the system? Use elimination.
____ 15. 5x + 7y = 32
8x + 6y = 46
a. (1, 5) b. (7, 0) c. (8, 5) d. (5, 1)
How many solutions does the system have?
____ 16. x − 2y = 6
3x − 6y = 18
a. one solution b. two solutions c. infinitely many solutions d. no solution
____ 17. Mike and Kim invest $12,000 in equipment to print yearbooks for schools. Each yearbook costs $5 to print
and sells for $15. How many yearbooks must they sell before their business breaks even?
a. 800 yearbooks b. 1,200 yearbooks c. 2400 yearbooks d. 1,800 yearbooks
Multiple Response
Identify one or more choices that best complete the statement or answer the question.
____
1. Which of these systems of equations would be best solved using the subtraction method?
Check all that apply
I.
3x - 4y = 0
-9x + 4y = -36
II.
2y = x - 2
y = 3x - 7
a. System III b. System II c. System I
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III.
-4x + 3y = 0
-4x - 9y = -36
Name: ________________________
ID: A
Short Answer
1. Solve the system of equations by substitution.
y = 3x - 10
3x + 2y = 16
2. River C is 100 miles longer than River D.
If the sum of their lengths is 5,500 miles, what is the length of each river?
Essay
1. A plane travels 236 miles in 2 hours against the wind. On the return trip, it travels the same 236 miles in 1
hour. Find the speed of the wind.
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