Free Printable Systems of Inequalities

Worksheets

Systems of Inequalities

Total questions: 15

Worksheet time: 4hrs 45mins

Name

Class

Date

Which point is a solution?

(0, 6)

(-3, 4)

(1, 0)

(-4, 3)

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

Solution

Not a solution

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

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

(0,-1)

(0,3)

(4,0)

(6,-2)

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

Which of the following points is a solution to the system of equations below?
x + 2y ≥ 4
3x − 2y < 4
Take your time!

(0, 0)

(2, 1)

(2, 2)

(-1, 1)

Write the system of inequalities
Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing

x+y≤300
7.5x+5.5y≥2000

x+y<300
7.5x+5.5y≥2000

x+y≤300
7.5x+5.5y≤2000

x+y>2000
7.5x+5.5y≤300

Solve the system of inequalities by graphing.

10.

Luka and Dana are making cookies for the Westland Pantry. They only have up to 6 hours to bake! They can bake 32 chocolate chip cookies in an hour (x), and 20 snickerdoodle cookies in an hour (y). They need to make at least 150 cookies. Which inequalities represent the situation?

x + y ≥ 6
32x + 20y ≤ 150

x + y ≥ 632
x + 20y ≥ 150

x + y ≤ 6
32x + 20y ≤ 150

x + y ≤ 6
32x + 20y ≥ 150

11.

Kate is selling bracelets and earrings on Etsy to make money for summer vacation. The bracelets (x) cost $2 and earrings (y) cost $3. She needs to make at least $100, but can only make up to 40 pieces of jewelry. Which inequalities represent this situation?

2x + 3y > 100

x + y ≤ 40

100x + 2y > 3

x + y ≤ 40

100x + 40y > 100

3x + 2y ≤ 40

3x + 2y > 100

x + y ≤ 40

12.

What's the difference between systems of equations and systems of inequalities?

Systems of equations have 1 solution, no solution, or infinite solutions while systems of inequalities can have a range of solutions.

Systems of equations use slope-intercept form only while systems of inequalities use standard form only.

Systems of equations have a shaded region while systems of inequalities do not.

There is no difference.

13.

Cole is doing a basketball challenge for charity. In order to win money for the charity, he needs to score at least 20 points in less than 10 shots. If x is the number of 2-point shots, and y is the number of three point shots, which inequalities below represent the situation?

x + y < 10

2x + 3y ≥ 20

x + y ≤ 10

2x + 3y ≥ 20

x + y ≤ 10

2x + 3y > 20

x + y < 10

2x + 3y > 20

14.

JoAnn likes her job as a baby-sitter, but it pays only $3 per hour. She has been offered a job as a tutor that pays $6 per hour. Because of school, her parents only allow her to work a maximum of 15 hours per week. How many hours can JoAnn tutor and baby-sit and still make at least $66 per week? How much does she make?

b + t < 15
3b + 6t > 66

b + t > 15
3b + 6t < 66

3b + 6t > 15
b + t < 66

3b + 6t < 15
b + t < 66

15.

Luka and Dana are making cookies for the Westland Pantry. They only have up to 6 hours to bake! They can bake 32 chocolate chip cookies in an hour (x), and 20 snickerdoodle cookies in an hour (y). They need to make at least 150 cookies. Which one of these is a valid solution?

3 chocolate chip and 2 snickerdoodle

1 chocolate chip and 4 snickerdoodle

2 chocolate chip and 8 snickerdoodle

5 chocolate chip and 1 snickerdoodle

100 %

Systems of Inequalities

Total questions: 15

Worksheet time: 4hrs 45mins

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