Free Printable Ch. 6 Systems of Equations & Inequalities (Complete)

Worksheets

Ch. 6 Systems of Equations & Inequalities (Complete)

Total questions: 120

Worksheet time: 30hrs 0mins

Name

Class

Date

Solve for x and y
3x + 2y = 16
7x + y = 19

(-2,5)

(-2,-5)

(2,-5)

(2,5)

Solve for x and y
y = 2x + 1
y = 4x - 1

(1,3)

(-1,-3)

(-1,3)

(3,1)

If a system of equations has no solution, what does the graph look like?

intersecting lines

parallel lines

skew lines

intersecting lines

What is the solution of the two linear equations shown?

(2,2)

(0,0)

(1,2)

None of these

When you graph the exact same equation twice,

you will have no solution.

you will have one solution.

you will have infinite solutions.

you will graph a giraffe.

Solve for x and y
5x + 3y = 7
y = 4

(4,1)

(4,-1)

(1,4)

(-1,4)

Solve:
y = 2x -11
-3y = -6x -15

(-1.5,-4)

(1.5,4)

No solution (parallel lines)

Infinitely many solutions

Which inequality is graphed on the given coordinate plane?

y > x + 1

y < x + 1

y ≥ -x + 1

y ≤ -x + 1

Which ordered pair(s) is a solution to the given system?

(5, -5)

(0,0)

(-5, -2)

(3,-3)

10.

Which ordered pair(s) is a solution to the given system?

(5,0)

(1,-3)

(3,3)

(2,1)

11.

Rewrite this inequality in "y=" form to graph.
3x - 6y > 12

y > ¹/₂x - 2

y < -¹/₂x + 2

y < ¹/₂x - 2

y > -3x - 2

12.

Nicole has 15 nickels and dimes. If the value of her coins is $1.20, how many of each coin does she have?

6 dimes, 9 nickles

9 dimes, 6 nickles

10 dimes, 5 nickles

5 dimes, 10 nickles

13.

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?

x+y=134
x+y=120

3x+3y=134
4x+3y=120

4x+3y=134
3x+3y=120

7xy=134
6xy=120

14.

Two brothers went shopping at a back-to-school sale where all shirts and shorts were the same price. The younger brother spent $175 on 7 new shirts and 7 pairs of shorts. The older brother purchased 6 new shirts and 7 pairs of shorts and paid a total of $165. How much did one shirt cost?

$10

$15

$20

15.

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.

x + y = 33
y = 2x - 3

x + y = 33
x = 2y - 3

x + y = 33
x = 3 - 2y

x + y = 3
x = 33 - 2y

16.

Sarah makes small purses (x) and big purses (y). She can make no more than 8 purses a week.
Which inequality represents the situation?

x + y ≤ 8

x + y ≤ 6

2x + 3y ≤ 6

x + y ≤ 10

17.

Use substitution to solve the system of equations.

x - 7y = 11
5x + 4y = -23

(-3, -2)

(-4, 1)

(4, -1)

(3, 2)

18.

Use elimination to solve the system of equations.
2x + 3y = 5
6x + 9y = 15

(-2, 3)

(7, 3)

No Solution

Infinite Solutions

19.

Determine the correct system of equations represented in the graph above.

2x - 4y = 12
x + y = 3

-2x + 4y = 12
-x - y = -3

2x - 3y = 0
2x - y = 4

2x + 3y = 0
2x + y = 4

20.

Which system of linear inequalities represents the graph seen above?

y≤ ½x - 1
y > 2x - 4

y > ½x - 1
y ≤ 2x - 4

y < ½x - 1
y ≥ 2x - 4

y ≥ ½x - 1
y < 2x - 4

21.

Solve the system of inequalities by graphing and describe regions of intersection.
y ≥ - 4x + 8
y < -4x + 4

The graphs have an overlapping region below the first inequality and above the second inequality.

The graphs have an overlapping region above the first inequality and below the second inequality.

The regions of the inequalities entirely overlap.

The graphs of the inequalities do not overlap, there is no solution to the system.

22.

What is the solution?

(1, -1)

(-1, 1)

(0, -2)

(0, 1)

23.

There are 50 donkeys and chickens on a farm. There are a total of 174 legs. Which system below can be used to figure out how many of each animal the farm has?

d + c = 174
4d + 2c = 50

d + c = 50
4d + 2c = 174

d + c = 50
2d + 4c = 174

d + c = 174
2d + 4c = 50

24.

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?

3x + 2y = 315
2x + 4y = 450

3x + 2y = 450
2x + 4y = 315

2x + 2y = 315
3x + 4y = 450

25.

Your family goes to a southern style restaurant for dinner. There are 6 total people in your family. Some order chicken for $14 and the rest order steak for $17. The total bill is $99. Write a system that could represent this situation.

c + s = 6
14c + 17s = 99

c + s = 99
14c + 17s = 6

c + s = 6
17c + 14s = 99

c + s = 99
17c + 14s = 6

26.

Solve using substitution.
x - 2y = 2
3x + 4y = 3

(1.4, -0.3)

(3.1, 5)

(-2.5, 3.5)

(6.9, 1.02)

27.

Solve using substitution.
2x - 2y = 2
y = -5x + 14

(4, 5)

(2.5, 1.5)

(1.5, 5)

(1, 2.25)

28.

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

Yes, they are part of the solution set

No, they are NOT part of the solution set

29.

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

It has an equal sign.

The symbol is greater than.

The symbol has "or equal to."

You just guess.

30.

Which point is a solution?

(0, 6)

(-3, 4)

(1, 0)

(-4, 3)

31.

Match: the overlap is on the left!

y ≤ 3x and y ≤ -2x + 4

y > 3x and y > -2x + 4

y < 3x and y > -2x + 4

y > 3x and y < -2x + 4

32.

Select the correct graph for each inequality.

33.

y < x−2
y < 3

y > -x+2
y > 3

y < -x+2
y < 3

y < -x+2
y > 3

34.

Which system of inequality is shown?

y ≥ -x - 1
y < x + 4

y < -x - 1
y ≥ x + 4

y > -x - 1
y ≥ x + 4

y = -x - 1
y ≥ x + 4

35.

You can work at most 20 hours next week. You need to earn at least $92 to cover you weekly expenses. Your math tutoring job pays $7.50 per hour and your job as a pet sitter pays $6 per hour. You can work at most 7 hours tutoring. Write a system of linear inequalities to model the situation.

s + t < 20
6s + 7.50t ≥ 92
t >7

s + t ≤ 20
6s + 7.50t ≥ 92
t ≤ 7

36.

What is the solution?

(6, 3)

(3, 6)

(-6, 3)

No solution

37.

38.

Which system of equations represents the graph?

y = -3/5x - 3
y = 3x - 3

y = - 5/3 x + 3
x - 3y = 9

39.

195 copies

301 copies

196 copies

300 copies

40.

x + y = 3

x + y = 4

2x + y = 5

4x + 2y = 10

2x + y = 7

4x - 2y = 14

3x - y = 2

x - 3y = -2

41.

( -3, -9)

( -7, -11)

( -4, -7)

( -1, -10)

42.

y < x + 3

8x + y < -8

y < x + 8

3x + y > -8

y > x + 8

3x + y < -8

y > x + 3

8x + y > -8

43.

infinitely many solutions

one solution

no solutions

44.

500 yearbooks

520 yearbooks

400 yearbooks

1,740 yearbooks

45.

( 1, 1)

( 2, 1)

( 3, 0)

( 3, 4)

46.

47.

( 1, 7)

( -3, 3)

( -6, -3/2 )

( 4, -11)

48.

49.

50.

( 3, -3)

( 3, -4)

( 6, -2)

( 4, 6)

51.

40 mi/h

32 mi/h

8 mi/h

48 mi/h

52.

length = 5 cm

width = 18cm

length = 13 cm

width = 5 cm

length = 13 cm

width = 8 cm

length = 18 cm

width = 5 cm

53.

207 copies

206 copies

420 copies

421 copies

54.

30 nickels and 32 dimes

30 nickels and 28 dimes

29 nickels and 31 dimes

31 nickels and 29 dimes

55.

rose bush = $13

ornamental grass = $5

rose bush = $10

ornamental grass = $11

rose bush = $9

ornamental grass = $12

rose bush = $12

ornamental grass = $9

56.

Approximately 38 customers;
$375 profit with 60 customers.

Approximately 38 customers;
$7135 profit with 60 customers.

Approximately 45 customers;
$375 profit with 60 customers.

Approximately 45 customers;
$7135 profit with 60 customers.

57.

Maximum = $200;
Minimum = $40

Maximum = $105;
Minimum = $85

Maximum = $125;
Minimum = $70

Maximum = $110;
Minimum = $80

58.

Write a system of inequalities to represent the solution of the above diagram. How many points with integer coordinates are solutions of the system?

y ≥ 2x - 6
y ≤ -0.5x + 4;
y ≥ -3x - 6;
14

y ≤ 2x - 6
y ≤ -0.5x + 4;
y ≥ -3x - 6;
47

y ≤ 2x - 6
y ≤ -0.5x + 4;
y ≥ -3x - 6;
14≥

y ≥ 2x - 6
y ≤ -0.5x + 4;
y ≥ -3x - 6;
47

59.

Which of the following is not a method to solve systems?

Elimination

Difference of Squares

Substitution

Graphing

60.

If I were to solve for x in the second equation, what would be the only step?

-7x - 2y = (-13)

x - 2y = 11

Add x

Subtract 11

Subtract 2y

Add 2y

61.

4x - 2y = 7

x + 2y = 3

If I had to solve using substitution, which variable should I solve for?

y in the first equation

y in the second equation

x in the second equation

x in the first equation

62.

4x+8y=20

-4x+2y=-30

Which method would be easiest way to solve this system of equations?

graphing

linear programming

substitution

elimination

63.

3x + 2y = 16

7x + y = 19

If I had to solve using substitution, which variable should I solve for?

y in the first equation

y in the second equation

x in the first equation

x in the second equation

64.

2x − 3y = −1

y = x − 1

Which method would be the easiest to use to solve this system of equations?

substitution

elimination

65.

Solve using elimination:

6x - 4y = 28

2x + 2y = 6,

x = 1, y = 2

x = 2, y = 1

x = -4, y = 1

x = 4, y = -1

66.

Caitlin won a bag full of money! She has 49 bills in all. She counts $1,430. There are $20 dollar bills and $50 dollar bills. How many of each bill does Caitlin have?
WRITE a system where T= # of $20 and F = # of $50.

T + F = 1430
20T + 50F = 49

T+ F = 49
10T + 5F = 1430

T + F = 49
20T + 50F = 1430

T + F = 49
T + F = 1430

67.

It takes Sarah 2 hours to make small purses and 3 hours to make big purses. She has a maximum of 18 hours a week. Which inequality represents this situation?

2x + 3y ≤ 18

x + y ≤ 6

x + y ≤ 9

3x + 2y ≤ 18

68.

Due to the face that Sarah cannot make a negative number of purses, what other constraints does she have?

x≥0

y≥0

x≤0

y≤0

69.

What are the two linear inequalities graphed here?

y ≤ - x + 4
y < x - 2

y ≤ - x + 4
y > x - 2

y ≤ - 2x + 4
y > 2x - 2

y ≤ - x + 2
y > x - 4

70.

Which would be correct describing the solution for this graph of two inequalities?

Any point that is NOT in the pink or blue is a solution to this system.

Any point that falls in either the pink or blue is a solution to the system.

Only a point that is on either boundary line is a solution to this system.

There is no point that is a solution to this system.

71.

Which points are solutions to the system shown?

(5, 3) (6, -3)

(3, 3) (5, -3)

(-2, 2) (-4, 4)

(1, 2) (1, 5)

72.

Find the solution to the system
y = x - 1
y = 2x - 2

(-3, 0)

(-4, -3)

(-3, 4)

(1, 0)

73.

What is the solution to this system?

(-1, -2)

(-2, -1)

There is no solution.

There are infinite solutions.

74.

An exam worth 145 points contains 50 questions. Some questions are worth two points and some are worth five points. How many five point questions are on the test?

75.

What type of solution does the system below have?
8x - 4y = 12
y = 2x - 3

One solution

No solution

Infinite solutions

76.

What type of solution does this system have?
2y - 30x = -6
-3y + 45x = 15

One solution

No solution

Infinite solutions

77.

Will my line be solid?
5 ≥ x

Yes

78.

Which point below is NOT part of the solution set?

(0, 0)

(5, 1)

(-1, -3)

(20, -5)

79.

Select the correct graph for each inequality.

80.

Select the correct graph for each inequality.

81.

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

Solution

Not a solution

82.

Which point is a solution?

(0, 6)

(-3, 4)

(1, 0)

(-4, 3)

83.

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

(0,-1)

(0,3)

(4,0)

(6,-2)

84.

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

Solution

Not a solution

85.

Which of the following inequalities matches the given graph?

x ≥ -1

x ≤ -1

x > -1

x < -1

86.

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

Yes, they are part of the solution set

No, they are NOT part of the solution set

87.

Which point below is NOT part of the solution set?

(0, 0)

(5, 1)

(-1, -3)

(20, -5)

88.

Which system of inequalities matches the graph?

y > 2x - 4
y < 2

y < 2x - 4
y < 2

y > 2x - 4
y < 2

y < 2x - 4
y < -2

89.

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

(1, -5)

(2, 3)

(-2, 3)

(-1, 1)

90.

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

(-1, -3)

(3, 0)

(-2, 2)

(4, 1)

91.

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

(0, 0)

(1, 1)

(-4, -2)

(4, -2)

92.

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

(0, -2)

(-3, 0)

(-3, 2)

(1, 1)

93.

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

(0, 0)

(-3, 0)

(2, -5)

(3, -1)

94.

When you graph an inequality, you used a solid line when you use which symbols?

≤, ≥

<, >

95.

When graphing an inequality, you use a dotted line when you use which symbol?

<, >

≤, ≥

96.

Lisa and Tammy are selling items at the craft show. Which might be a reasonable solution from the graph showing the number of items sold when they both have earned the same amount?

(1, 12)

(3, 19)

(5, 25)

(0, 10)

97.

Which of the following equations match the given graph?

y ≥ 2/5x + 1

y ≥ -2/5x + 1

y≤ 2/5x + 1

y ≥ -2/5x - 1

98.

Which system of linear inequalities is represented by the graph?

y≤2x-1
y>-2x+3

y>2x-1
y≤-2x+3

y<2x-1
y≥-2x+3

y≤2x-1
y>2x+3

99.

Solve the system of inequalities by graphing.

100.

Colin needs to save at least $200 for homecoming. He works 2 jobs earning $9/hour at Wawa and $25/hour mowing lawns. He only has time to work 16 hours before homecoming.

x + y ≥ 25

x + y ≤ 9

100x + 25 y ≤ 200

2x + 9y ≤ 16

x + y ≥ 200

9x + 25y ≤ 16

9x + 25y ≥ 200

x + y ≤ 16

101.

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

TRUE

FALSE

102.

Match the system to the graph (solution set is on the left)

y ≤ 3x and y ≤ -2x + 4

y > 3x and y > -2x + 4

y < 3x and y > -2x + 3

y > 3x and y < -2x + 4

103.

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?

104.

Solve the system of inequalities by graphing.

105.

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?

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

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

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

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

106.

Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all. Upon completing the job he counted out the coins and it came to $6.60. Which system of equations could be used to find the exact number of dimes and nickels?

d + n = 6.60
.10d + .05n = 80

d + n = 80
d + n = 6.60

d + n = 80
.10d + .05n = 6.60

d + n = 80
.05d + .10n = 6.60

107.

If a system of linear equations has one solution, what does this mean about the two lines?

Parallel lines

the same line

Intersecting lines

108.

Solve the following system of equations by graphing:

(4, -4)

(-4, 4)

no solutions

(0, 0)

109.

Solve the following system of equations by graphing:

Infinite solutions

(2, -2)

(1, 0)

(3, -4)

110.

Solve the following system of equations using the elimination method:

(-2, 1)

no solutions

(-2, 0)

(-1, -3)

111.

Solve the following system of equations using the elimination method.

infinite solutions

(0, -2)

no solutions

(0, 2)

112.

Solve the system using any method.
−4x − 4y = 0
4x + 4y = 0

(−6, −4)

Infinite number of solutions

No solutions

(6, 4)

113.

Solve by elimination:
3x+7y=23

-3x-7y=-17

No solution

ARN

(-3,3)

(3,3)

114.

Solve by graphing:
y=5x+3

y=-2x-4

(2,-1)

(-1,-2)

(1,-2)

(-2,-1)

115.

How can you tell if a point is a solution to a system?

It makes the first equation true.

The (x,y) coordinates satisfy both equations

It makes logical sense

It makes neither equation negative

116.

Is (-3, -2) a solution to this system?

Yes

117.

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

Yes

118.

Graph the system.

119.

Graph the system.

120.

Which system of inequalities matches the graph?

x> -2
y < -4

x< 2
y> 4

x > 2
y < 4

x > 2
y <- 4

100 %

Ch. 6 Systems of Equations & Inequalities (Complete)

Total questions: 120

Worksheet time: 30hrs 0mins

Similar Resources on Wayground