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6.1- 6.4 Review Systems of Equations

Total questions: 83

Worksheet time: 18hrs 15mins

Name
Class
Date
1.

Which graph represents a system of equations with infinite solutions?

a)
b)
c)
d)

None of the above

2.

Which graph represents a system of equations with no solution?

a)
b)
c)
d)

None of the above

3.
Buzz graphed two lines in order to find the solution to a given system of equations.
What is the solution?
a)
(-1, 4)
b)
(1, -4)
c)
(-4, 1)
d)
(4, -1)
4.

Does the system have one, none or infinite solutions?

y = 2x -11

y = 2x +5

a)

One

b)

None

c)

Infinitely many solutions

5.

Solve the solution by substitution:

x = 7 - 2y

2x + y = 5

a)

(-1,4)

b)

(4,-1)

c)

(1,3)

d)

(3,1)

6.
What is the solution to the system of equations? 
y = 3x - 8
y = 4 - x
a)
(3,1)
b)
(1,3)
c)
(-3,1)
d)
(3,-1)
7.
Solve the system of equations using substitution:
-4x + 4y = 8
y = -2x - 10
a)
(-4, -2)
b)
(12, -34)
c)
(4, -18)
d)
(-2, -6)
8.
Solve by elimination:
4x+9y=28
-4x-y=-28
a)
(-7,0)
b)
(6,0)
c)
(-6,0)
d)
(7,0)
9.
Solve by elimination:
-9x-4y=-20

5x+4y=4
a)
(-4,4)
b)
(4,4)
c)
(4,-4)
d)
(-4,-4)
10.
Solve by elimination:
7x+y=-9

-3x-y=5
a)
No solution
b)
(1,8)
c)
(-2,-3)
d)
(-1,-2)
11.
What is the solution to the system?
a)
(0, 3)
b)
(1, -1)
c)
(-3, 1)
d)
(1, 3)
12.
Solve the system by elimination. 
 −4x − 4y = 0
4x + 4y = 0 
a)
(−6, −4) 
b)
Infinite number of solutions  
c)
(−6, 10) 
d)
(6, 4) 
13.
Solve by elimination
-12x-4y= -8 
  -6x-2y= -4
a)
no solution 
b)
(0,0)
c)
infinite solutions 
d)
(4,0)
14.
Solve the system by elimination.  

−8x − 10y = 20
−8x − 6y = −4 
a)
Infinite number of solutions  
b)
(6, 5) 
c)
(−6, −5) 
d)
(5, −6) 
15.
Which method would be best (quickest) for solving the system below:
x + y = 11
3x - 4y = -2
a)
Substitution
b)
Elimination
c)
Graphing
d)
None of these
16.
What is the solution to the system?
a)
(0, 3)
b)
(1, -1)
c)
(-3, 1)
d)
(1, 3)
17.
When does a system of equations have no solutions?
a)
When the lines cross
b)
When slopes of the lines are different
c)
When the slopes are the same
d)
There is ALWAYS a solution sir!
18.
Which method would be best (quickest) for solving the system below:
3x - 4y = -2
y = 2x + 1
a)
Substitution
b)
Elimination
c)
Graphing
d)
None
19.
Which method would be best (based on their  for solving the system below:
y = 2x - 5
y = (-1/4)x + 17
a)
Graphing
b)
Elimination
c)
Not possible
20.
Solve the system:
2x + 3y = -2
3x - 2y = 23
a)
(5, -4)
b)
(-4, 5)
c)
(-5, 4)
d)
infinite solutions
21.
How can you tell if a point is a solution to a system?
a)
It makes the first equation true.
b)
The (x,y) coordinates satisfy both equations
c)
It makes logical sense
d)
It makes neither equation negative
22.

Is the point (2, -1) a solution to the systems of equations below?


y=5x+3


y=-2x-4

a)

Yes

b)

No

23.

Is the points (-4, 4) a solution to the system of equations?

a)

Yes

b)

No

24.
Will the solution (-3, -7) make the following system of equations a true statement? 
y = 4x + 5
y = x – 4
a)
YES
b)
NO
25.
Determine if (4, 1) is a solution for the system of equations.
y = -x + 5
y = 2x - 7
a)
yes
b)
no
26.

Identify the solution for the system of equations.

a)

(1, -2)

b)

(-1, 2)

c)

(-1, -2)

d)

(1, 2)

27.

Identify the solution for the system of equations.

a)

(3, 1)

b)

(1, 3)

c)

(-1, -3)

d)

(-3, -1)

28.

Is (1,10) a solution to

y=7x+5

y=x+9

a)

yes

b)

no

29.

Is (1,7) a solution for

y=3x+4

y=x+6

a)

yes

b)

no

30.

Is the ordered pair (2,1) a solution to the system?

a)

Yes

b)

No

31.

Is the ordered pair (4, -1) a solution to the system of equation?

a)

Yes

b)

No

32.

Find the slope and y - intercept

y = 1/2x - 1

a)

slope: 1/2 y-intercept: -1

b)

slope: 2 y-intercept: -1

c)

slope: 1/2x y-intercept: 1

d)

slope: 2 y-intercept: 5

33.
Solve:
y=8x+1
y=6x+3
a)
(1, 9)
b)
(4, 14)
c)
(0, 1)
d)
(2, 4)
34.
Determine whether the ordered pair is a solution of y=2x-4.
(-4,5)
a)
Yes
b)
No
35.

I am confident with most of this material... [rank how you feel]

a)

1. I don't know any of this...

b)

2. I am comfortable with some, but need some assistance

c)

3. I am okay at most of this.

d)

4. I am confident with most of this.

36.

Your family goes to a restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14.80, and some order steak for $17. If the total bill was $91, which system best represents the situation?

a)

x + y = 6

14.80x + 17y = 91

b)

x + y = 91

14.80x + 17y = 6

c)

x + y = 6

14.80y + 17x = 91

d)

x + y = 91

14.80x+ 17y = 6

37.
Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total. Solve the system:
x + y = 21
6x + 4y = 104
a)
(10, 11)
b)
(12, 9)
c)
(11, 10)
d)
(9, 12)
38.
David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?
a)
(35, 52)
b)
(18, 69)
c)
( 52, 35) 
d)
(61, 26)
39.
At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, t, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?
a)
t + n = 54
t = 3n + 8
b)
t + n = 54
n = 3t + 8
c)
t + n = 54
t = 3n - 8
d)
t + n = 8
t = 3n + 54
40.
The equations of two lines are 6x + y = 26 and y = 2x + 10. If the solution is (2, y), what is the value of y? 
a)
14
b)
4
c)
6
d)
2
41.

The sum of Mr. Micklow and Ms. Craft's age is 55. The difference is 3. Ms. Craft is older than Mr. Micklow. How old is Ms. Craft?

a)

23

b)

26

c)

29

d)

32

42.

8 + x = 10

a)

18

b)

2

c)

10

d)

8

43.

4 = 2 + x

a)

6

b)

2

c)

8

d)

4

44.

w - 13.7 = 22.8

a)

36.5

b)

9.1

c)

11.1

d)

42.5

45.

n + 25\frac{2}{5} =  45\frac{4}{5}  

a)

65\frac{6}{5}  

b)

25\frac{2}{5}  

c)

1151\frac{1}{5}  

d)

2

46.

16 = m - 14

a)

30

b)

2

c)

20

d)

12

47.

5x = 10

a)

50

b)

2

c)

5

d)

15

48.

6 = 3x

a)

2

b)

18

c)

3

d)

9

49.

3v = 18

a)

6

b)

16

c)

15

d)

54

50.

z16=8\frac{z}{16}=8  

a)

128

b)

2

c)

24

d)

100

51.

a)

60

b)

50

c)

70

d)

80

52.

The Maplewood Symphony Orchestra sold 146 tickets and collected a total of $1036 in ticket sales. Admission was $5 for children and $8 for adults. Write two equations that would be used to solve the system.

a)

c+a=146

5c+8a=1036

b)

c-a=146

8c+5a=1036

c)

c+a=1036

8c+5a=146

d)

c+a=146

5c-8a=1026

53.

The manager of a movie theater wants to know the number of adults and children who go to the movies. The theater charges $8 for each adult and $4 for each child. At a showing where 200 tickets were sold, the theater collected $1304. Write two equations that would be used to solve the system.

a)

a+c=1304

8a+4c=200

b)

a+c=200

4a+8c=1304

c)

a+c=200

8a+4c=1304

d)

a-c=200

4a+8c=1304

54.

J. P. is thinking of two numbers. The sum of the numbers is 163, and their difference is 33. Write two equations that would be used to solve the system.

a)

x+y=33

x+y=163

b)

x+y=163

x-y=33

c)

x-y=33

x-y=163

d)

x+y=33

x-y=163

55.

The school’s photographer took pictures of couples at this year’s prom. She charged $3.25 for wallet-size pictures and $10.50 for portrait-size pictures. Crystal and Dan bought a total of 10 pictures for $61.50. Write two equations that would be used to solve the system.

a)

10.50w+3.25p=10

w+p=61.50

b)

3.25w+10.50p=10

w+p=61.50

c)

10.50w+3.25p=61.50

w+p=10

d)

3.25w+10.50p=61.50

w+p=10

56.

On Friday, 3247 people attended the county fair. The entrance fee was $5 for adults and $3 for children 12 or under. The fair collected a total of $14,273. Write two equations that would be used to solve the system.

a)

3a+5c=3,247

a-c=14,273

b)

5a+3c=14,273

a+c=3,247

c)

3a-5c=3,247

a+c=14,273

d)

5a+3c=3,247

a+c=14,273

57.

Each day Mario prepares a large basket of self-serve tortilla chips in his restaurant. On Monday, 40 adults and 15 children ate 10.8 lb of chips. On Tuesday, 35 adult and 22 children ate 12.29 lb of chips. Write two equations that would be used to solve the system so that Mario would know whether adults or children eat more chips on average.

a)

15a-40c=12.29

35a+22c=10.8

b)

40a+15c=10.8

35a+22c=12.29

c)

15a+40c=10.8

35a-22c=12.29

d)

40a+15c=12.29

35a+22c=10.8

58.

Eric has some quarters and nickels in his pocket. He has 8 more nickels than quarters. The total value is $3.70. Write two equations that could be used to solve the system.

a)

0.25q+0.05n=3.70

q=n+8

b)

0.05q+0.25n=3.70

n=q+8

c)

0.25q+0.05n=3.70

n=q+8

d)

0.25q-0.05n=3.70

n=q-8

59.

Nancy went to the grocery story. On Monday she purchased 4 apples and 6 bananas for a total of $13. On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50. Which system of equations represents the situation?

a)

4x + 6y = 3

13.5x - 13y = 6

b)

x + y = 4

x - y = 6

c)

4x + 6y = 13

3x + 7y = 13.5

d)

4x - 6y = 13

3x - 7y = 13.5

60.
The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75. Write a system of equations.
a)
5q + 2z = 1.32
1z = 0.75
b)
5q + 2z = 1.32
3q + 1z = 0.75
c)
q + z = 1.32
q + z = 0.75
d)
5q + 2z = 0.75
3q + 1z = 1.32
61.
What is the definition of function?
a)
Has inputs and outputs
b)
Every input has only ONE output
c)
Inputs have different outputs every time
d)
x-values and y-values
62.
Does this mapping diagram represent a function?
a)
No, because an input value goes to multiple output values
b)
Yes, because each input goes to one and only one output
63.
Is the relation a function? Why.
a)
Yes, because the x-value 11 has two y-values pair with it.
b)
Yes, because each x-value has only one y-value paired with it.
c)
No, because the x-value 11 has two y-values pair with it.
d)
No, because each x-value has only one y-value paired with it.
64.
Which set of values is a function?
a)
(9,5) (10,5) (9,-5) (10,-5)
b)
(3,4) (4,-3) (7,4) (3, 8)
c)
(6,-5) (7, -3) (8, -1) (9, 1)
d)
(2, -2) (5, 9) (5, -7) (1, 4)
65.
Which set of values is a function?
a)
(9,5) (10,5) (9,-5) (10,-5)
b)
(3,4) (4,-3) (7,4) (3, 8)
c)
(6,-5) (7, -3) (8, -1) (9, 1)
d)
(2, -2) (5, 9) (5, -7) (1, 4)
66.
Is this graph a function or not a function? 
a)
Function 
b)
Not a Function
67.
Which graph does NOT pass the vertical line test?
a)
Graph 1
b)
Graph 2
c)
Graph 3
d)
Graph 4
68.
a)
Function
b)
Not a Function
69.
a)
Function
b)
Not a Function
70.
Is this table a function or not a function? 
a)
Function
b)
Not a Function
71.
5x+1=2x-5
a)
x=-2
b)
x=-6
c)
x=3
d)
x=.5
72.
2x-1=3x+8
a)
x=7
b)
x=-9
c)
x=5
d)
x=3
73.
4x+9=-2x-15
a)
x=-4
b)
x=-24
c)
x=-6
d)
x=1
74.
4a-2=3a-7
a)
a=-9
b)
a=-2
c)
a=7
d)
a=-5
75.
1x-6=2x+3
a)
x=-9
b)
x=3
c)
x=9
d)
x=2
76.

21=3+4n+5n21=3+4n+5n  

a)

9

b)

−7-7  

c)

6

d)

2

77.

−118=−5(4+7x)+7-118=-5\left(4+7x\right)+7  

a)

−5-5  

b)

−9-9  

c)

33  

d)

−1-1  

78.

97=−3(6n−5)−897=-3\left(6n-5\right)-8  

a)

−10-10  

b)

1616  

c)

−5-5  

d)

−2-2  

79.
4 = 2(x + 3)
a)
1/2
b)
7/2
c)
-1
d)
5
80.

10(h+1) - 4 = 76

a)

h=10

b)

h=4

c)

h=7

d)

h=76

81.
What is the first step to solve this equation:
11 - 3x = 44
a)
Add 3 to both sides
b)
Subtract 11 from both sides
c)
Add 11 to both sides
d)
Divide 3 on both sides.
82.
Solve for x:
5x - 14 = 8x + 4
a)
x = 6
b)
x = -6
c)
x = -18/13
d)
x = 10/3
83.
6z = 49 - z
a)
49
b)
-7
c)
6
d)
7

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