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Inequalities And System Of Equations

Systems TEST

Systems TEST

Presentation

•

Mathematics

•

11th Grade

•

Easy

Created by

Brandon Berk

Used 2+ times

FREE Resource

8 Slides • 102 Questions

1

Systems

Of Equations

Of Inequalities

TEST 3A: This test covers several topics including (but not limited to) Systems of Equations, Inequalities, and Word Problems.

2

Section 1:

System Basics

and Solving EQ's

3

Multiple Choice

7(2x - 4) = 42

1

x= 5

2

x= 8

3

x= 2

4

x= 9

4

Multiple Choice

8v - 4(v + 8) = 8

1

2

2

10

3

4

4

-4

5

Multiple Choice

Solve:
3x + 15 = 3(x + 5)

1

No Solution

2

x = 15

3

Infinitely Many Solutions

6

Open Ended

In Mathematics, what is a System? (define system of equations)

Type response here

7

Multiple Choice

A system has ____________ when two lines intersect at one point.

1

One solution

2

No solution

3

Infinitely Many Solution

8

Multiple Choice

A system has ____________ when two equations are exactly the same and overlap each other.

1

One solution

2

No solution

3

Infinitely Many Solution

9

Multiple Choice

A system has ____________ when two equations have same slope but different y-intercept and are parallel.

1

One solution

2

No solution

3

Infinitely Many Solution

10

Multiple Choice

Which of these is NOT one of the methods I showed you for solving systems of linear equations?

1

Elimination

2

Substitution

3

Graphing

4

Frustration

11

Section 2:

Systems of Equations Graphing

12

Multiple Choice

To find a solution by graphing is to find the point where two lines intersect.

1

True

2

False

13

Multiple Choice

Question image

What is the solution to the system?

1

(6, 8)

2

(8, 6)

3

(-6, 8)

4

No solution

14

Multiple Choice

Question image

What is the solution to the system?

1

(2, -2)

2

(2, 2)

3

(-2, 2)

4

(-2, -2)

15

Multiple Choice

Question image

What is the solution to the system?

1

Infinitely Many Solutions

2

No Solution

3

(0, 0)

4

(-3, 0)

16

Multiple Choice

Question image

^{What is the solution?}

1

1

2

-2

3

(1, 2)

4

(1, -1)

17

Multiple Choice

Question image

What is the solution to the system?

1

(0, 3)

2

(1, -1)

3

(-3, 1)

4

(1, 3)

18

Multiple Choice

Question image

What is the solution to this system?

1

(-2, -2)

2

(2, -2)

3

(-2,2)

4

(2, 2)

19

Multiple Choice

The solution (x, y) to a system of equations is the point where they...?

1

Run off the graph

2

Don't touch

3

Intersect

4

Exist

20

Multiple Choice

When does a system of equations have no solutions?

1

When the lines cross

2

When slopes of the lines are different

3

When the slopes are the same

4

There is ALWAYS a solution sir!

21

Multiple Choice

Parallel lines have ____ solution(s).

1

No

2

One

3

Many

22

Multiple Choice

Intersecting lines have _____ solution(s).

1

No

2

One

3

many

23

Multiple Choice

Two equations that produce the same line have _____ solution(s).

1

no

2

one

3

infinitely many

24

Section 3:

Systems of Equations Substitution

25

Multiple Choice

Question image

Solve by using substitution method.

1

(2, 7)

2

(0, 1)

3

(2/5, 9/5)

4

(2, 5)

26

Multiple Choice

Question image

For equations below, which method is easier to use? Why?

1

Graphing, because both are already in y = mx + b form.

2

Substitution, because one equation is already solved for y.

3

Elimination, because both are already in ax + by = c form.

4

None.

27

Multiple Choice

Question image

Solve each system by substitution.

1

A

2

B

3

C

4

D

28

Multiple Choice

Question image

Solve each system by substitution.

1

A

2

B

3

C

4

D

29

Multiple Choice

Question image

Solve each system by substitution.

1

A

2

B

3

C

4

D

30

Multiple Choice

Question image

Solve each system by substitution.

1

A

2

B

3

C

4

D

31

Multiple Choice

Question image

Solve each system by substitution.

1

A

2

B

3

C

4

D

32

Multiple Choice

Question image

Solve each system by substitution.

1

A

2

B

3

C

4

D

33

Multiple Choice

Question image

Solve each system by substitution.

1

A

2

B

3

C

4

D

34

Multiple Choice

Question image

Solve each system by substitution.

1

A

2

B

3

C

4

D

35

Multiple Choice

Question image

Solve each system by substitution.

1

A

2

B

3

C

4

D

36

Multiple Choice

Question image

Solve each system by substitution.

1

A

2

B

3

C

4

D

37

Multiple Choice

Question image

Solve each system by substitution.

1

A

2

B

3

C

4

D

38

Section 4:

Systems of Equations Elimination

39

Multiple Choice

Question image

Solve by using elimination method.

1

(3, 1)

2

( 5, -5)

3

(2, 5)

4

(15, 1)

40

Multiple Choice

Solve using elimination.
4x + 8y = 20
-4x + 2y = -30

1

(-7,1)

2

(2,-5)

3

(-2,5)

4

(7,-1)

41

Multiple Choice

Solve the system by elimination.

−8x − 10y = 20
−8x − 6y = −4

1

Infinite number of solutions

2

(6, 5)

3

(−6, −5)

4

(5, −6)

42

Multiple Choice

-4x - 6y = 6
4x + 6y = -4

1

no solution

2

(2,0)

3

(-4,0)

4

(0,0)

43

Multiple Choice

Solve the system of Equation (x,y)
3x + 2y = –13
3x + 4y = 1

1

(-9,7)

2

(7,-9)

3

(4,-7)

4

(-7,-4)

44

Multiple Choice

-4x-2y=-12
4x+8y=-24

1

(5,6)

2

(6,-6)

3

(6,-2)

4

(4,-3)

45

Multiple Choice

4x+8y=20
-4x+2y=-30

1

(-7,1)

2

(2,-5)

3

(-2,5)

4

(7,-1)

46

Multiple Choice

Solve by elimination
-12x-4y= -8
-6x-2y= -4

1

no solution

2

(0,0)

3

infinite solutions

4

(4,0)

47

Multiple Choice

Solve the system by elimination.
−4x − 4y = 0
4x + 4y = 0

1

(−6, −4)

2

Infinite number of solutions

3

(−6, 10)

4

(6, 4)

48

Multiple Choice

Solve by elimination
-2x + 6y = 16
-4x - 3y = 2

1

(2,2)

2

(-2, -2)

3

(-2,2)

4

(2,1)

49

Fill in the Blank

Use the elimination strategy to find the points that these two equations will meet (write your answer as a point)

2y - x=5

-3y+x = -9

Type your answer in the boxes

50

Multiple Choice

Solve the system of Equation (Elimination Method)
5x + y = 9
10x − 7y = −18

1

(-4,-1)

2

(-1,-4)

3

(4,1)

4

(1, 4)

51

Section 5:

Systems of Equations Inequalities

52

Multiple Choice

How can I tell if an inequality will have a solid line?

1

It has an equal sign.

2

The symbol is greater than.

3

The symbol has "or equal to."

4

You just guess.

53

Multiple Choice

y ≥ -2x - 2 will have what type of line

1

dashed

2

solid

54

Multiple Choice

y < x - 2 will have what kind of line?

1

dashed

2

solid

55

Multiple Choice

y < 6x + 1 will have what kind of line?

1

dashed

2

solid

56

Multiple Choice

x ≥ 2 will have what type of line?

1

dashed

2

solid

57

Multiple Choice

y ≥ 5 will have what type of line?

1

dashed

2

solid

58

Multiple Choice

y ≤ -3x +1 will have what type of line?

1

dashed

2

solid

59

Multiple Choice

y ≤ x - 2 will have what type of line?

1

dashed

2

solid

60

Multiple Choice

Question image

Are the points on the boundary line part of the solution set or not?

1

Yes, they are part of the solution set

2

No, they are NOT part of the solution set

61

Multiple Choice

Do I need to flip my sign?
2x - 3y ≥ 12

1

Yes

2

No

62

Multiple Select

Question image

According to the graph, which point is a solution? Choose all that apply.

1

(0, 0)

2

(4, 2)

3

(-1, -5)

4

(-3, 0)

63

Multiple Choice

Question image

Is the point (3, 1) a solution for the following inequality? Choose the best answer that has the best explanation.

1

Yes because it is located in the shaded region.

2

No because it is located on the line and the line is dotted.

3

Yes because it is located on the line.

4

No because it is in the shaded region.

64

Multiple Choice

Which inequality below is equivalent to

3x - y > 4

1

y > 3x - 4

2

y < -3x + 4

3

y < 3x - 4

4

y > -3x + 4

65

Multiple Select

When graphing $y<\frac{3}{5}x-4$ , you will draw which of the following.

1

A dotted line

2

A solid line

3

Shade up

4

Shade down

66

Multiple Select

When graphing $y\ge-\frac{2}{7}x+1$ , you will draw which of the following.

1

A dotted line

2

A solid line

3

Shade up

4

Shade down

67

Multiple Choice

Question image

Randy must graph x + 3y > 6. Part of his effort is shown in the graph. Which of the following is true about Randy's work so far?

1

All is great so far. He just needs to do the shading part.

2

He has the incorrect y-intercept indicated since it should be at (0, 6).

3

His "rise over run" technique is incorrect since it is reversed.

68

Multiple Choice

Identify the y-intercept for the function:
y=-3x

1

-3

2

0

3

1

4

-1

69

Multiple Choice

How can I tell if an inequality will have a solid line?

1

It has an equal sign.

2

The symbol is greater than.

3

The symbol has "or equal to."

4

You just guess.

70

Multiple Choice

Do I need to flip my sign?
3x ≥ 12

1

Yes

2

No

71

Multiple Choice

Which ordered pair is a solution of the inequality?

y ≥ 4x – 5

1

(3, 4)

2

(3, 0)

3

(2, 1)

4

(1, 1)

72

Multiple Choice

Question image

Which point below is NOT part of the solution set?

1

(0, 0)

2

(-10, 20)

3

(3, 5)

4

(0, -2)

73

Multiple Choice

How can I tell if an inequality will have a dashed boundary line?

1

It does not have an equal sign.

2

The symbol is less than than.

3

The symbol does not have "or equal to."

4

You just guess.

74

Multiple Choice

Question image

Which inequality describes this graph...

1

y < 3x - 2

2

y > 3x + 2

3

y < 3x + 2

4

y > 3x -2

75

Multiple Choice

Question image

This is a graph of which inequality?

1

y > 4x - 2

2

y > -2x + 4

3

y < -2x

4

y < 4X - 2

76

Multiple Choice

Question image

Choose the correct inequality for this graph.

1

2

3

4

77

Multiple Choice

Question image

Which graph best represents the following inequality?

1

2

3

4

78

Multiple Choice

Question image

Determine whether point A is a solution to the linear inequality that is shown.

1

Yes

2

No

3

Sometimes

79

Multiple Choice

Question image

Solve the system of inequalities by graphing.

1

2

3

4

80

Multiple Choice

Question image

Solve the system of inequalities by graphing.

1

2

3

4

81

Multiple Choice

Question image

Which point is a solution?

1

(0, 6)

2

(-3, 5)

3

(1, 0)

4

(-4, 3)

82

Multiple Choice

Question image

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

1

Solution

2

Not a solution

83

Multiple Choice

Question image

Is (-2,4) a solution to the system?

1

Solution

2

Not a solution

84

Multiple Choice

Question image

Which of the following is not a solution to this system of inequalities?

1

(0,-1)

2

(0,3)

3

(4,0)

4

(6,-2)

85

Multiple Choice

Question image

Which of the following is a solution to the systems of inequalities?

1

(1, -5)

2

(2, 3)

3

(-2, 3)

4

(-1, 1)

86

Multiple Choice

Question image

Which of the following is a solution to the systems of inequalities?

1

(0, 0)

2

(1, 1)

3

(-4, -2)

4

(4, -2)

87

Multiple Choice

Question image

Which of the following is a solution to the systems of inequalities?

1

(0, 0)

2

(-3, 0)

3

(2, -5)

4

(3, -1)

88

Multiple Choice

Question image

Which system of inequalities matches the graph?

1

x> -2 y < -4

2

x< 2 y> 4

3

x > 2 y < 4

4

x > 2 y <- 4

89

Multiple Choice

Tell whether the ordered pair
(-3, 0) is a solution of the given system.
y ≤ x + 4
y ≥ 2x - 6

1

Yes

2

No

90

Multiple Choice

Question image

Which system of inequalities matches the graph?

1

y > 2x - 4 y < 2

2

y < 2x - 4 y < 2

3

y > 2x - 4 y < 2

4

y < 2x - 4 y < -2

91

Multiple Choice

Will my line be solid?
5 ≥ x

1

Yes

2

No

92

Multiple Choice

Question image

Which of the following inequalities matches the given graph?

1

x ≥ -1

2

x ≤ -1

3

x > -1

4

x < -1

93

Multiple Choice

Question image

This system of inequalities has an infinite number of solutions, TRUE or FALSE?

1

TRUE

2

FALSE

94

Multiple Choice

Question image

How many solutions does the system of linear equations shown have?

1

0

2

1

3

2

4

Infinite

95

Multiple Choice

Question image

Write an inequality represented by the graph.

1

x < - 3

2

y < - 3

3

x > - 3

4

x ≥ - 3

96

Fill in the Blank

What is the slope-intercept form of the equation

6x – 3y = 12

Type your answer in the boxes

97

Section 6:

Systems of Equations Word Problems

98

Multiple Choice

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?

1

4x + 6y = 3 13.5x - 13y = 6

2

x + y = 4 x - y = 6

3

4x + 6y = 13 3x + 7y = 13.5

4

4x - 6y = 13 3x - 7y = 13.5

99

Multiple Choice

Amy sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Adam sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60. What is the price of 1 pack of sugar cookies and 1 pack of oatmeal cookies?

1

Sugar Cookies $5 Oatmeal Cookies $3

2

Sugar Cookies $4 Oatmeal Cookies $8

3

Sugar Cookies $2 Oatmeal Cookies $6

4

Sugar Cookies $3 Oatmeal Cookies $6

100

Multiple Choice

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?

1

(35, 52)

2

(18, 69)

3

( 52, 35)

4

(61, 26)

101

Multiple Choice

On the first night, the Movie House Theater sold 7 adult tickets and 11 child tickets for $227. On the second night they took in $150 by selling 6 adult tickets and 6 child tickets. Find the price of an adult ticket and the price of a child ticket.

1

Adult $13 Child $5

2

Adult $10 Child $6

3

Adult $8 Child $16

4

Adult $12 Child $13

102

Multiple Choice

Josh is thinking of two numbers. Their sum is -10 and their difference is -2. Which system of equations represents the situation?

1

x - y = -10 x + y = -2

2

x = -2 y = 5

3

x + y = -2 x - y = -10

4

x + y = -10 x - y = -2

103

Multiple Choice

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?

1

x + y = 6 14.80x + 17y = 91

2

x + y = 91 14.80x + 17y = 6

3

x + y = 6 14.80y + 17x = 91

4

x + y = 91 14.80x+ 17y = 6

104

Multiple Choice

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50. It turns out that the doughnuts were more popular than the coffee. On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25. Which equations could be used to determine the cost of the coffee?

1

10c + 5d = 14.25 5c + 10d = 16.50

2

10c + 5d = 16.50 5c + 10d = 14.25

3

c + d = 10 5c + 10d = 16.50

4

c + d = 5 5c + 10d = 16.50

105

Open Ended

Create a System of Equations STORY PROBLEM of your own.

Solve the System and include the solution in your answer.

Type response here

106

Section 7:

Systems

REVIEW

107

Poll

How well do you feel you understand this "System's of Equations" Unit

1 - I have no clue what's going on

3 - I kinda get it, but have lots of questions

5 - I've GOT THIS

1

2

3

4

5

108

Open Ended

What is something that went well this unit?

Type response here

109

Open Ended

What is something that you should do differently for the next units?

Type response here

110

Open Ended

What can Mr Berk do to help you better in the next units?

Type response here

Systems

Of Equations

Of Inequalities

TEST 3A: This test covers several topics including (but not limited to) Systems of Equations, Inequalities, and Word Problems.

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