Free Printable System of Inequalities Mixed Review

1.

Solve the system of inequalities by graphing.

a)

b)

c)

d)

2.

Which point is a solution?

a)

(0, 6)

b)

(-3, 4)

c)

(1, 0)

d)

(-4, 3)

3.

Identify the graph represented by the following system of inequalities.

2x - y > 4

4x + 2y < 6

a)

b)

c)

4.

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

a)

Solution

b)

Not a solution

5.

Which system of inequalities matches the graph?

a)

x> -2
y < -4

b)

x< 2
y> 4

c)

x > 2
y < 4

d)

x > 2
y <- 4

6.

Which region of the graph represents the solution set to the system of inequalities below?

$y\le\frac{1}{2}x+2$

$-y>-3x-1$

a)

Region A

b)

Region B

c)

Region C

d)

Region D

7.

Which of the following linear inequalities represents the graph?

a)

$y\ge3x$

b)

$y>3x$

c)

$y<3x$

d)

$y>\frac{1}{3}x$

8.

Which of the following linear inequalities represents the graph?

a)

$y\ge3$

b)

$x\ge3$

c)

$y\le3$

d)

$y<3$

9.

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

a)

x + y ≤ 300
7.5x + 5.5y ≥ 2000

b)

x + y < 300
7.5x + 5.5y ≥ 2000

c)

x + y ≤ 300
7.5x + 5.5y ≤ 2000

d)

x + y > 2000
7.5x + 5.5y ≤ 300

10.

Jonah is going to the store to buy candles. Small candles cost $3.50, and large candles cost $5.00. He needs to buy at least 20 candles and cannot spend more than $80.

Write a system of linear inequalities that represents the situation.

a)

$x+y\le20$

$3.5x+5y\ge80$

b)

$xy\ge20$
$3.5+5y\le80$

c)

$x-y\ge20$
$3.5x+5y\le80$

d)

$x+y\ge20$
$3.5x+5y\le80$

11.

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?

a)

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

b)

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

c)

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

d)

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

12.

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

a)

x + y ≤ 300

7.5x + 5.5y ≥ 2000

b)

x + y < 300

7.5x + 5.5y ≥ 2000

c)

x + y ≤ 300

7.5x + 5.5y ≤ 2000

d)

x + y > 2000

7.5x + 5.5y ≤ 300

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?

a)

x + y < 10

2x + 3y ≥ 20

b)

x + y ≤ 10

2x + 3y ≥ 20

c)

x + y ≤ 10

2x + 3y > 20

d)

x + y < 10

2x + 3y > 20

14.

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?

a)

x + y ≥ 6
32x + 20y ≤ 150

b)

x + y ≥ 632
x + 20y ≥ 150

c)

x + y ≤ 6
32x + 20y ≤ 150

d)

x + y ≤ 6
32x + 20y ≥ 150

15.

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?

a)

x + y < 10

2x + 3y ≥ 20

b)

x + y ≤ 10

2x + 3y ≥ 20

c)

x + y ≤ 10

2x + 3y > 20

d)

x + y < 10

2x + 3y > 20

16.

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)

17.

Consider the function y<2x+3. Which is true?

a)

The line would be solid with shading above.

b)

The line would be dashed with shading above.

c)

The line would be solid with shading below.

d)

None of these.

18.

Write the inequalities

a)

x≤-2
y≤x-3

b)

y≤-2
y≤x-3

c)

x≥-2
y≤x-3

d)

y≥-2
y≤x-3

19.

Write the inequalities

a)

y≥-2x+3
y≤x-3

b)

y>2x+3
y≥x-3

c)

y>-2x+3
y≥x-3

d)

y<-2x+3
y≤x-3

20.

Which point is a solution?

a)

(0, 6)

b)

(-3, 5)

c)

(1, 0)

d)

(-4, 3)

System of Inequalities Mixed Review

Total questions: 20

Worksheet time: 1hrs 21mins

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