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Systems of Equations Review

Total questions: 65

Worksheet time: 5hrs 24mins

Name
Class
Date
1.
Which equation represents the following graph?
a)
y = 3x + 2
b)
y = -2x + 3
c)
y = 2x + 3
d)
y = -3x + 2
2.
What is the solution to this system?
a)
(1, -1)
b)
(-1, 1)
c)
(0, -2)
d)
(2, 0)
3.
How many solutions will this system have? 
a)
No solution
b)
One Solution
c)
I Don't Know
d)
Infinitely Many Solutions
4.
If a system of linear equations has one solution, what does this mean about the two lines? 
a)
Parallel lines
b)
the same line 
c)
Intersecting lines
5.
What is the solution to this system?
a)
One Solution
b)
No solution
c)
Infinitely Many Solutions
6.
The solution (x, y) to a system of equations is the point where they...? 
a)
Run off the graph
b)
Don't touch
c)
Intersect
d)
Exist
7.

Which system of linear equations has no solution?

a)
b)
c)
8.

What is the solution to the following system of equations? (Remember to put parentheses in your answer).

(a)  

9.
Parallel Lines never intersect because...
a)
they have the same slopes. 
b)
they have the same y-intercept.
c)
they have different slopes.
d)
they have different y-intercepts. 
10.
What is the solution?
a)
(6, 3)
b)
(3, 6)
c)
(-6, 3)
d)
No solution
11.
What is the solution? 
a)
1
b)
-2
c)
(1, 2)
d)
(1, -1)
12.
The ordered pair that satisfies (makes them true) all equations in the system is a called a ________________.
a)
system of equations
b)
function
c)
graph
d)
solution of a system
13.
What is the solution?
a)
No solution
b)
(0, 2)
c)
(0, -4)
d)
(3, -3)
14.

What is 'b' in this linear equation? y= 5x - 6

a)

6

b)

5

c)

y

d)

-6

15.
What type of slope?
a)
undefined
b)
positive slope
c)
negative slope
d)
zero slope
16.

Solve this system by substitution.

a)

(1, -4)

b)

(1, 4)

c)

(-4, -7)

d)

(-7, -4)

17.
What is the solution to this system of equations?
a)
(4, -1)
b)
(-1, 4)
c)
(-4, 1)
d)
(-4, -1)
18.
The first step in solving using the substitution method is __________.
a)
get x by itself
b)
get y by itself
c)
get either variable by itself
d)
add the equations together
19.
How many solutions will this system have? 
a)
No solution
b)
One Solution
c)
I Don't Know
d)
Infinitely Many Solutions
20.

Solve the system of equations.

4x+9y=28

-4x-y=-28

a)

(-7,0)

b)

(6,0)

c)

(-6,0)

d)

(7,0)

21.

Solve the system of equations.

7x+y=-9

-3x-y=5

a)

No solution

b)

(1,8)

c)

(-2,-3)

d)

(-1,-2)

22.
The solution (x, y) to a system of equations is the point where they...? 
a)
Run off the graph
b)
Don't touch
c)
Intersect
d)
Exist
23.

3x + y = –14

–2x – y = 9

Which method would be best for solving this system?

a)

Substitution

b)

Elimination

24.

Which is the best method to use?


y = 6x − 11

−2x − 3y = −7

a)

Graphing

b)

Substitution because a variable is isolated.

c)

Elimination because both equations are in standard form.

25.
Solve for x and y.
y = 2/3x - 2
y = -x + 3
a)
(0,3)
b)
(0,-3)
c)
(3,0)
d)
(-3,0)
26.

Is (1,10) a solution to

y=7x+5

y=x+9

a)

yes

b)

no

27.
Solve for x and y
3x + 2y = 16
7x + y = 19
a)
(-2,5)
b)
(-2,-5)
c)
(2,-5)
d)
(2,5)
28.
What is the value of the y-coordinate of the solution to the system of equations 
x-2y=1
x+4y=7 
a)
1
b)
-1
c)
3
d)
4
29.

Solve the following systems of equations using substitution:


2y + x = -15

x = 3y

a)

(-3, -9)

b)

(-9, -3)

c)

(-3, 9)

d)

(9, -3)

30.
There are 15 animals in a barn.  These animals are horses and chickens.  There are 44 legs in all.  Which system of equations represents the situation?
a)
x + y = 15
4x + 2y = 44
b)
4x + 2y = 15
x + y = 44
c)
x = 2y + 44
4x = y + 15
d)
2x - 4y = 44
x - y = 15
31.
Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, choose the system that matches the situation.
a)
x + y = 33
y = 2x - 3
b)
x + y = 33
x = 2y - 3
c)
x + y = 33
x = 3 - 2y
d)
x + y = 3
x = 33 - 2y
32.

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

33.
The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?
a)
S + A = 530
3S + 4A = 1740
b)
S + A = 530
4S + 3A = 1740
c)
S + A = 1740
3S + 4A = 530
d)
S + A = 1740
4S + 3A = 530
34.

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

35.

Caitlin won a bag full of money! She has 49 bills in all. She counts $1430. There are twenty dollar bills and fifty dollar bills. How many of each bill does Caitlin have? Which system best represents the situation?

a)

x + y = 1430

20x + 50y = 49

b)

x + y = 49

10x + 5y = 1430

c)

x + y = 49

20x + 50y = 1430

d)

x + y = 49

x + y = 1430

36.
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
37.
Christian had brochures printed for a new business venture. Christian originally ordered 4 boxes of black-and-white brochures and 3 boxes of color brochures, which cost a total of $134. After those ran out, Christian spent $120 on 3 boxes of black-and-white brochures and 3 boxes of color brochures. Which system represents this situation?
a)
x+y=134
x+y=120
b)
3x+3y=134
4x+3y=120
c)
4x+3y=134
3x+3y=120
d)
7xy=134
6xy=120
38.
Give the solution to the system.
a)
(3,1)
b)
(1,3)
c)
(-1,3)
d)
(1, -3)
39.
A ________________ is a set of two or more equations that have the same variables.
a)
solution of a system
b)
elimination method
c)
system of equations
d)
table
40.

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. Which system of equations represents the situation?

a)

3H + 2D = 315

2H + 4D = 450

b)

3H + 2D = 450

2H + 4D = 315

c)

2H + 4D = 315

3H + 2D = 450

d)

3H + 2D = 315

2H + 2D = 135

41.

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)

1.5N+0.5S=78.5

N+S=87

b)

1.5N+0.5S=78.5

1.5N+0.5S=87

c)

N+S=78.5

1.5N+0.5S=87

d)

N+S=78.5

N+S=87

42.
There are 50 donkeys and chickens on a far.  There are a total of 174 legs.  Which system below can be used to figure out how many of each animal the farm has?
a)
d + c = 174
4d + 2c = 50
b)
d + c = 50
4d + 2c = 174
c)
d + c = 50
2d + 4c = 174
d)
d + c = 174
2d + 4c = 50
43.
Solve for y:
5x + y = -10
a)
y = 5x + 10
b)
y = -5x - 10
c)
y = 2
d)
y = -5
44.
Solve for y:
2x + 2y = 6
a)
y = - x + 3
b)
y = x + 3
c)
y = 2x +6
d)
y = - 2x + 6
45.
Solve for y: 
4x + 3y = 9
a)
y = -3/4x + 3
b)
y = -4x + 9
c)
y = -4/3x + 3
d)
3y = -4x + 9
46.
Solve for y:
7x+ 2y = 20
a)
y= 7/2x + 10
b)
y=-7/2x + 10
c)
y=2/7 x- 10
d)
y= -2/7x + 10
47.
Solve for y: 
8x + 4y= 16
a)
y = -8x + 16
b)
y = 2x -4
c)
y = -2x + 4
d)
y = -8x + 12
48.

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child ticket

a)

3S+C=38

3S+2C=52

b)

3S+C=52

3S+2C=38

c)

3C+S=38

3C+2S=52

d)

3C+S=52

3C+2S=38

49.

What is the best method do you use?

y = 6x − 11

−2x − 3y = −7

a)

Graphing

b)

Substitution because a variable is defined

c)

Elimination because both equations are in standard form.

50.

What is the best method to use?

2x − 3y = −1

y =x − 1

a)

Graphing

b)

Substitution because a variable is defined

c)

Elimination because the equations are in standard form.

51.

What is the best method to use?

−4x − 2y = −12

4x + 8y = −24

a)

Graphing

b)

Substitution because a variable is defined

c)

Elimination because the equations are in standard form.

52.

What is the best method to use?

y = −3x + 5

5x − 4y = −3

a)

Graphing

b)

Substitution because a variable is defined

c)

Elimination because the equations are in standard form

53.

What is the best method to use?

4x + 8y = 20

−4x + 2y = −30

a)

Graphing

b)

Substitution because a variable is defined

c)

Elimination because the equations are in standard form

54.

What variable do you eliminate?


4x + 8y = 20

−4x + 2y = −30

a)

X because they have opposite signs

b)

Y because they have opposite signs

55.

What is the proper set up to solve the equation?

-7x -2y= -13

x = 2y+11

a)

-7(11) -2y = -13

b)

-7(2y +11)-2y = -13

c)

-7x -2(11) =-13

d)

-7x - 2(2y+11)= -13

56.

What variable do you eliminate, and what do you multiply the equation(s) by?

5x + y = 9

10x − 7y = −18

a)

You eliminate x, and multiply the top equation by -2

b)

You eliminate y, and multiply the top equation by 7

57.

What variable do you eliminate and how?

7x + 2y = 24

8x + 2y = 30

a)

You pick x because it's LCM is 56

b)

You pick y because it's LCM is 2.

58.
Steffen graphed two lines in order to find the solution to a given system of equations.
What is the solution?
a)
(-3,-8)
b)
(-8,-3)
c)
(3,-8)
d)
(8,3)
59.
Solve for x and y
5x + 3y = 7
y = 4
a)
(4,1)
b)
(4,-1)
c)
(1,4)
d)
(-1,4)
60.
Solve for x and y
3x + 2y = 16
7x + y = 19
a)
(-2,5)
b)
(-2,-5)
c)
(2,-5)
d)
(2,5)
61.
Solve the system of equations.
y = 4x+1
3x + 2y = 13
a)
(1, 5)
b)
(5, 1)
c)
(0.25, 2)
d)
∅
62.
Solve the system given:
3x - y = 7
2x + y = 3
a)
(-1,2)
b)
(5,4)
c)
(4,5)
d)
(2,-1)
63.

Solve the system:

y= 3x -13

2x +4y =4

a)

(5,2)

b)

(4, -1)

c)

(-4, -1)

d)

(5, -2)

e)

(-4, 1)

64.

Solve the system:

x+ 3y = 9

2x+ y = −2

a)

(3,2)

b)

(-2, 2)

c)

(3, -4)

d)

(-3, 4)

e)

(0.5, -3)

65.

Solve the system:

y=5x−5

y= −4x+22

a)

(1, 2)

b)

(3, 10)

c)

(-1, 2)

d)

(-3, 10)

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