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M1 Unit 4 Review (Systems of Equations)

Total questions: 92

Worksheet time: 6hrs 41mins

Name
Class
Date
1.
What is the solution?
a)
No solution
b)
(0, 2)
c)
(0, -4)
d)
(3, -3)
2.
Where do these two lines intersect?
a)
No solution
b)
(-2, 3)
c)
(3, -2)
d)
(2, 3)
3.
These two lines intersect at _____.
a)
(4, -2)
b)
(4, 2)
c)
(-2, 4) 
d)
No solution
4.
What is the system's solution?
a)
(-9, -5)
b)
(-5, -9)
c)
(9, -5)
d)
No solution
5.

Solve the system of equations by graphing.

a)

(4, 7)

b)

(3, 5)

c)

(6, 7)

d)

(5, 3)

6.

Solve the system of equations by graphing.

a)

(2, -5)

b)

(2, 5)

c)

(4, -6)

d)

(-2, -3)

7.
Solve by elimination 
-2x + 6y = 16
-4x  - 3y = 2
a)
(2,2)
b)
(-2, -2) 
c)
(-2,2)
d)
(2,1)
8.
Solve using elimination. 
 4x + 8y = 20
-4x + 2y = -30
a)
(-7,1)
b)
(2,-5)
c)
(-2,5)
d)
(7,-1)
9.
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) 
10.
-4x - 6y = 6
4x + 6y = -4
a)
no solution
b)
(2,0)
c)
(-4,0)
d)
(0,0)
11.

Solve for x and y by using the substitution method.


y = 2x + 1

y = 4x - 1

a)

(1,3)

b)

(-1,-3)

c)

(-1,3)

d)

(3,1)

12.

Solve for x and y by using the substitution method.


3x + 2y = 16

y = -7x + 19

a)

(-2,5)

b)

(-2,-5)

c)

(2,-5)

d)

(2,5)

13.

Solve for x and y by using the substitution method.

y = -2x

4x - y = 0

a)

(1,2)

b)

(0,0)

c)

No Solutions

d)

Infinite Solutions

14.

Solve the system by using the substitution method

a)

(3, 6)\left(3,\ 6\right)

b)

(6, 3)\left(6,\ 3\right)

c)

(1, 4)\left(1,\ 4\right)

d)

(4, 1)\left(4,\ 1\right)

15.

Is (0,0) a solution to the system?

a)

Solution

b)

Not a solution

16.

Which point is a solution to the system of inequalities?

a)

(-8,2)

b)

(-2,-5)

c)

(0,6)

d)

(4, 3)

17.
Which inequality is shown in the graph?
a)
y < 2x + 1
b)
y < -2x + 1
c)
y ≤ 2x + 1
d)
y ≤ -2x + 1
18.

What is the inequality symbol for the equation of this boundary line?

a)

less than

b)

less than or equal to

c)

greater than

d)

greater than or equal to

19.
Which system of inequalities is shown?
a)
y ≥ -x - 1
y < x + 4
b)
y < -x - 1
 y ≥ x + 4
c)
y > -x - 1
y ≥ x + 4
d)
y > -x - 1
y ≥ x + 3
20.
Match
a)
y < x−2 
y < 3
b)
y > -x+2
y > 3
c)
y < -x+2
y < 3
d)
y < -x+2
y > 3
21.

When graphed, the line will be...

5 ≥ x

a)

Solid

b)

Dashed

c)

Zig-Zag

22.
If a system of equations has no solution, what does the graph look like? 
a)
intersecting lines
b)
parallel lines
c)
skew lines
d)
intersecting lines
23.
Solve the system by substitution.
 
5x + 4y= −14
y =  −7x  −  15 
a)
(-2, -1)
b)
(1, -2)
c)
(-2, 1)
d)
(-1, -2)
24.

Solve the system by substitution.

x + 2y = 2

x = -4y + 2

a)
(-3, 0)
b)
(0, 2)
c)
(-3, -2)
d)
(2, 0)
25.
Solve by elimination:
4x+9y=28
-4x-y=-28
a)
(-7,0)
b)
(6,0)
c)
(-6,0)
d)
(7,0)
26.

Solve the system using elimination.

2x + 3y = 12

5x - y = 13

a)

(-3, -2)

b)

(1.5, 2)

c)

(3, 0)

d)

(3, 2)

27.
Which point is a solution?
a)
(0, 6)
b)
(-3, 4)
c)
(1, 0)
d)
(-4, 3)
28.
Is (-2,4) a solution to the system?
a)
Solution
b)
Not a solution
29.
Which point is a solution?
a)
(0, 6)
b)
(-3, 4)
c)
(1, 0)
d)
(-4, 3)
30.
Which of the following is not a solution to this system of inequalities?
a)
(0,-1)
b)
(0,3)
c)
(4,0)
d)
(6,-2)
31.

The owner of Mark's Meat Market orders beef and chicken. He wants to but at least 50 pounds of meat but cannot spend more than $300. Beef is $3 a pound and chicken is $2 a pound.
Which system of inequalities models this situation?

a)

x + y ≤\le 50
2x + 3y >> 300

b)

x + y ≥\ge 50
3x + 2y ≤\le 300

c)

x + y << 300
2x + 50 ≥\ge 300

d)

x - y ≤300\le300
3x + 2y ≤\le 50

32.
You have a total of 17 coins.  All of your coins are nickels and dimes.  The total value of the coins is $1.35.  Which system of equations represents this situation?
a)
n+d=17
.05n+.10d=1.35
b)
.05n+.10d=17
n+d=1.35
c)
.25n+.10d=1.35
n+d=17
33.

At a restaurant, the cost for 2 burritos and 1 tortilla salad is $20.57. The cost for 3 burritos and 3 tortilla salads is $36.24. Which pair of equations can be used to determine b, the cost of a burrito, and t, the cost of a tortilla salad?

a)

b + t = 20.57


3b + 3t = 36.24

b)

2b + t = 20.57


3b + 3t = 36.24

c)

2b + t = 20.57


b + t = 36.24

d)

b + 2t = 20.57


b + t = 36.24

34.

Solve the system of equations using the substitution method:
x + 2y = 7
2x - y = 1

a)

(2, 2.5)

b)

(3, 2)

c)

(1, 3)

d)

(2, 3)

35.

Determine the solution to the system of equations by elimination:
3x - 5y = 11
2x + 5y = 1

a)

(3, -1)

b)

(1, 3)

c)

(2, 2)

d)

No solution

36.

Which of the following represents the graph of the inequality?
y > 3x + 2

a)

y < 3x + 2

b)

y ≤ 3x + 2

c)

y > 3x + 2

d)

y ≥ 3x + 2

37.
What are systems of linear equations?
a)
a set of two or more linear equations in the same variables
b)
a polynomial with three terms
c)
set of two or more linear inequalities in the same variables
38.
If a system of equations has no solution, what does the graph look like? 
a)
intersecting lines
b)
parallel lines
c)
skew lines
d)
intersecting lines
39.
What is the solution?
a)
(1, -1)
b)
(-1, 1)
c)
(0, -2)
d)
(2, 0)
40.
When you graph the exact same equation twice,
a)
you will have no solution. 
b)
you will have one solution.
c)
you will have infinite solutions. 
d)
you will graph a giraffe. 
41.
How many solutions will this system have? 
a)
No solution
b)
One Solution
c)
I Don't Know
d)
Infinitely Many Solutions
42.
What is the solution? 
a)
1
b)
-2
c)
(1, 2)
d)
(1, -1)
43.
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
44.

Solve the following system of equations by graphing:

a)

(4, -4)

b)

(-4, 4)

c)

no solutions

d)

(0, 0)

45.

Solve the following system of equations by graphing:

a)

Infinite solutions

b)

(2, -2)

c)

(1, 0)

d)

(3, -4)

46.

Solve the following system of equations using the elimination method:

a)

(-2, 1)

b)

no solutions

c)

(-2, 0)

d)

(-1, -3)

47.

Solve the following system of equations using the elimination method.

a)

infinite solutions

b)

(0, -2)

c)

no solutions

d)

(0, 2)

48.
How many solutions does this system of equations have?
a)
One Solution
b)
No solution
c)
Infinitely Many Solutions
d)
Two Solutions
49.
Solve for x and y
3x + 2y = 16
7x + y = 19
a)
(-2,5)
b)
(-2,-5)
c)
(2,-5)
d)
(2,5)
50.
Solve the system of equations by substitution.
y = -4x + 5
y =  3x - 16
a)
(-3, -25)
b)
(3,-7)
c)
(11, 17)
d)
(21, 47)
51.
Which of the following shows the solution to the system?
 y= -1/4x + 4
y = 2x + 2
a)
A
b)
B
c)
C
d)
D
52.

At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. If a system of equations is written, which would be the correct representation of the 2 variables?

a)

t: # of tacos

m: # of glasses of milk

b)

t: Cost of each taco

m: Cost of each glass of milk

c)

t: total cost

m: # of food items

d)

t: Cost of each glass of milk

m: Cost of each taco

53.
Solve the system using any method. 
 −4x − 4y = 0
4x + 4y = 0 
a)
(−6, −4) 
b)
Infinite number of solutions  
c)
No solutions
d)
(6, 4) 
54.
Solve by elimination:
3x+7y=23

-3x-7y=-17
a)
No solution
b)
ARN
c)
(-3,3)
d)
(3,3)
55.
Solve by graphing:
y=5x+3

y=-2x-4
a)
(2,-1)
b)
(-1,-2)
c)
(1,-2)
d)
(-2,-1)
56.
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
57.
Does the following system have One Solution, No Solution, or Infinite Solutions.  
y = 4x + 8
y = -5x + 3
a)
One solution
b)
No solution
c)
Infinite solution
58.
Parallel lines have the same slope with a different y-intercept and how many solutions?
a)
One
b)
No
c)
Infinite
59.
The same line on a graph, has how many solutions?
a)
One solution
b)
Infinite solutions
c)
No solution
60.
Intersecting lines have how many solutions?
a)
One solution
b)
No solutions
c)
Infinite solutions
61.
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)
62.
Solve for x and y
y = 2x + 1
y = 4x - 1
a)
(1,3)
b)
(-1,-3)
c)
(-1,3)
d)
(3,1)
63.
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
64.
Solve for x and y
3x + 2y = 16
7x + y = 19
a)
(-2,5)
b)
(-2,-5)
c)
(2,-5)
d)
(2,5)
65.
What is the solution to the system?
8x + 4y = 12
y = -2x + 3
a)
(0,3)
b)
(3,0)
c)
No solution(parallel lines)
d)
Infinitely many solutions
66.
Solve for x and y.
y = 2/3x - 2
y = -x + 3
a)
(0,3)
b)
(0,-3)
c)
(3,0)
d)
(-3,0)
67.
Solve the system of equations by elimination.
-x + y = -13
-8x - 4y = -8 
a)
(5, 8)
b)
(5, -8)
c)
(-5, -18)
d)
(-5, 8)
68.
Which of the following are ways to solve systems of equations? 
a)
Graphing
b)
Substitution
c)
Elimination
d)
All of the above
69.
Solve the system of equations by substitution.
y = -4x + 5
y =  3x - 16
a)
(-3, -25)
b)
(3,-7)
c)
(11, 17)
d)
(21, 47)
70.
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) 
71.
What is the solution?
a)
(1, -1)
b)
(-1, 1)
c)
(0, -2)
d)
(0, 1)
72.
Determine if (4, 1) is a solution for the system of equations.
y = -x + 5
y = 2x - 7
a)
yes
b)
no
73.
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)
1.5x+0.5y=78.5
x+y=87
b)
1.5x+0.5y=78.5
1.5x+0.5y=87
c)
x+y=78.5
1.5x+0.5y=87
d)
x+y=78.5
x+y=87
74.
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.  How long does it take her to do a haircut?
3x + 2y = 315
2x + 4y = 450
a)
45 minutes
b)
90 minutes
2x + 4y = 315
c)
60 minutes
3x + 4y = 450
d)
30 minutes
75.
Solve by the
Elimination method:
3x + y = -2
2x + y =  3
a)
(-5, 13)
b)
(13, 5)
c)
(5, -13)
76.
Last season two running backs on the Steelers football team rushed a combined total of 1550 yards.  One rushed 4 times as many yards as the other.  Let x and y represent the number of yards each individual player rushed. Which system of equations could be used? 
a)
x + y = 1550
y  = 4x
b)
x + y = 1550
y = x + 4
c)
y - x = 1550
y = 4x
d)
y = 1550 + x
y = x + 4
77.
The solution is:
a)
(4, 3)
b)
(3, 4)
c)
(-4, 3)
d)
No solution
78.
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)
79.
What is the solution to the system?
a)
(0, 3)
b)
(1, -1)
c)
(-3, 1)
d)
(1, 3)
80.
Lesly 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)
81.
y = -6x + 5
-2x + y = 5
a)
(-3, -6)
b)
(-6, 3)
c)
(0, 5)
d)
(-3, 5)
82.
6x + y = -1
y = -3x - 4
a)
(3, 1)
b)
(1, 7)
c)
(-3, 1)
d)
(1, -7)
83.
y = -3x + 11
5x + y = 21
a)
(1, -5)
b)
(1, 5)
c)
(-4, 5)
d)
(5, -4)
84.
3x + y = 1
y = 4x + 1
a)
(0, -1)
b)
No Solution
c)
(0, 8)
d)
(0, 1)
85.
Solve by elimination:
4x+9y=28
-4x-y=-28
a)
(-7,0)
b)
(6,0)
c)
(-6,0)
d)
(7,0)
86.
Solve by elimination:
7x+y=-9

-3x-y=5
a)
No solution
b)
(1,8)
c)
(-2,-3)
d)
(-1,-2)
87.
Solve by elimination
4x-6y= -6
-2x-12y= -12
a)
(0,1) 
b)
(1,0)
c)
(1,1)
d)
(2,1)
88.
Solve by elimination 
2x+9y= -7 
6x-3y= 9 
a)
(-1, -1) 
b)
(2,-1)
c)
(1,1)
d)
(1,-1)
89.

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

90.
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
91.
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)
92.
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)

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