Master Systems of Equations and Inequalities: Practice Quizzes and Tests

Question 1

Identify the point that satisfies the linear inequality y > 2x + 1:

Accepted Answer

(1, 5)

Answer

(2, 0)

Answer

(0, 1)

Answer

(-1, 3)

Question 2

Identify the inequality that represents the shaded region below the line y = 2x:

Accepted Answer

y < 2x

Answer

x > 2y

Answer

y > 2x

Answer

x < 2y

Question 3

Solve the system of inequalities: x ≥ 2 and y < -1.

Accepted Answer

The points outside the rectangle defined by the lines x = 2 and y = -1

Answer

The points inside the rectangle defined by the lines x = 2 and y = -1

Answer

The points on the line x = 2 and the line y = -1

Question 4

Graph the system of equations: x + 2y = 6 and 2x - y = 1.

Accepted Answer

Two intersecting lines

Answer

Two parallel lines

Answer

Two perpendicular lines

Answer

A single line

Question 5

Solve the system of inequalities:
 x ≥ 0
 y ≤ 3
 x + y ≤ 5

Accepted Answer

Solution region is the shaded triangle bounded by the lines x = 0, y = 3, and x + y = 5

Answer

Solution region is the area to the right of the line x = 0, below the line y = 3, and to the left of the line x + y = 5

Answer

Solution region is the area outside the shaded triangle bounded by the lines x = 0, y = 3, and x + y = 5

Question 6

Which of the following systems of equations has no solution ?

Accepted Answer

x + y = 1
x + y = 2

Answer

x + 2y = 4
2x + 4y = 8

Answer

2x + 3y = 6
x - y = 1

Answer

x + y = 5
x - y = 1

Question 7

Which of the following is an example of a linear inequality in two variables ?

Accepted Answer

2x + 3y ≤ 6

Answer

|x| > 5

Answer

x^2 + y^2 < 1

Answer

e^x + y = 10

Question 8

Solve the inequality:
 |x - 2| < 3

Accepted Answer

-1 < x < 5

Answer

x < -1 or x > 5

Answer

-5 < x < 1

Answer

x > -5 or x < 1

Question 9

Solve the system of equations:
x + y = 5
x - y = 1

Accepted Answer

(x, y) = (3, 2)

Answer

(x, y) = (1, 4)

Answer

(x, y) = (2, 3)

Question 10

Which of the following points is in the solution set of the system of inequalities:
x ≥ 2
y ≤ -1

Accepted Answer

(3, -2)

Answer

(-2, 1)

Answer

(0, 0)

Answer

(1, 2)

Question 11

Solve the system of equations:
x^2 + y^2 = 25
x - y = 3

Accepted Answer

(x, y) = (5, 2) or (x, y) = (2, 5)

Answer

x = 4, y = 3

Answer

x = 3, y = 4

Answer

x = 2, y = 5

Question 12

Which of the following systems of equations is inconsistent?

Accepted Answer

x + y = 5
x + y = 7

Answer

x^2 + y^2 = 25
x - y = 3

Answer

x - y = 2
x + y = 5

Answer

2x + y = 6
x - 2y = 3

Question 13

Which method is invalid for solving systems of linear equations?

Accepted Answer

Guess and Check

Answer

Elimination

Answer

Graphing

Answer

Substitution

Question 14

Identify the system of equations with no solution:

Accepted Answer

2x + y = 6
2x + y = 8

Answer

-x + 2y = 3
2x - 4y = 6

Answer

3x - 2y = 1
6x - 4y = 2

Answer

x + y = 5
x - y = 1

Question 15

Solve the following linear inequality:
2x - 5 > 11

Accepted Answer

x > 8

Answer

x > -8

Answer

x < 8

Answer

x < -8

Question 16

Graph the following compound inequality on a number line:
-2 < x ≤ 3

Accepted Answer

A closed circle at -2 and the region from -2 to 3 shaded

Answer

An open circle at -2 and the region from -2 to 3 shaded

Answer

A closed circle at -2 and the region from -2 to 3 not shaded

Question 17

Identify the point that lies within the solution region of the system of inequalities:
x + 2y ≥ 6
y ≤ -x + 3

Accepted Answer

(4, 1)

Answer

(-1, 0)

Answer

(2, 2)

Answer

(0, -1)

Question 18

Solve the following system of equations graphically: 
 2x - y = 4
 x + y = 5

Accepted Answer

The intersection point (3, 2)

Answer

The intersection point (-2, -3)

Answer

The intersection point (-3, -2)

Answer

The intersection point (2, 3)

Question 19

Translate the following word problem into a system of equations: 
John has twice as many apples as Mary. Together, they have 24 apples.

Accepted Answer

x = 2y 
x + y = 24

Answer

y = x / 2 
x + y = 24

Answer

x = y / 2 
x + y = 24

Answer

y = 2x 
x + y = 24

Question 20

Solve the inequality: 
|x - 3| > 2

Accepted Answer

x < 1 or x > 5

Answer

x < 1 or x < 5

Answer

x > 1 or x < 5

Question 21

Translate the following word problem into a system of equations: 
The sum of two numbers is 10. Their difference is 2.

Accepted Answer

x + y = 10 
x - y = 2

Answer

y - x = 10 
y + x = 2

Answer

x - y = 10 
x + y = 2

Answer

x + y = 2 
x - y = 10

Question 22

Graph the system of inequalities:

y ≤ x + 2
x ≥ -y - 1

Accepted Answer

[Image of a graph with shaded region bounded by the lines y = x + 2 and x = -y - 1]

Answer

[Image of a graph with no shaded region]

Answer

[Image of a graph with incorrect lines]

Answer

[Image of a graph with incorrect shaded region]

Question 23

Solve the system of inequalities:

x - 2y > 4
y < x + 1

Accepted Answer

[Image of a graph with shaded region bounded by the lines x - 2y = 4 and y = x + 1]

Answer

[Image of a graph with no shaded region]

Answer

[Image of a graph with incorrect lines]

Answer

[Image of a graph with incorrect shaded region]

Question 24

Solve the system of equations:

2x - 3y = 1
-x + 2y = 5

Accepted Answer

(2, 3)

Answer

(1, 4)

Answer

(3, 2)

Answer

(4, 1)

Question 25

Which of the following is a system of equations?

Accepted Answer

y = 2x + 1
x - y = 3

Answer

x^2 + y^2 = 1

Answer

y > x

Answer

x + y = 5

Question 26

Graph the following system of inequalities:

y > 2x
x + y < 5

Accepted Answer

Image of a shaded region above the line y = 2x and below the line x + y = 5

Answer

Image of a shaded region below the line y = 2x and above the line x + y = 5

Answer

Image of a shaded region to the left of the line y = 2x and to the right of the line x + y = 5

Question 27

Which of the following systems of equations has no solution?

Accepted Answer

2x + y = 3
2x + y = 5

Answer

3x - y = 6
y = 3x - 2

Answer

x + y = 2
y = x + 1

Answer

x - 2y = 1
2x - 4y = 2

Question 28

Which of the following is a linear inequality in two variables?

Accepted Answer

y > 2x - 1

Answer

|x - y| > 3

Answer

x^2 + y^2 < 1

Answer

sin(x + y) > 0

Question 29

Solve the following inequality:

2x - y < 4

Accepted Answer

Image of a shaded region below the line 2x - y = 4

Answer

Image of a shaded region to the left of the line 2x - y = 4

Answer

Image of a shaded region above the line 2x - y = 4

Answer

Image of a shaded region to the right of the line 2x - y = 4

Question 30

Solve the system of equations: 2x + y = 5 and x - y = 1

Accepted Answer

(2, 1)

Answer

(1, 3)

Answer

(3, -1)

Answer

(4, 0)

Question 31

Which point lies on the solution set of the inequality y < 2x + 1?

Accepted Answer

(0, 0)

Answer

(3, 2)

Answer

(1, 3)

Answer

(2, 1)

Question 32

A bakery sells cookies for $2 each and cupcakes for $3 each. A customer purchased 5 items and spent a total of $12. How many cookies did the customer purchase?

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 33

Find the solution to the system of equations represented by the graph: [Image of a graph of two intersecting lines]

Accepted Answer

(2, 1)

Answer

(1, 0)

Answer

(0, 1)

Answer

(1, 2)

Question 34

Which inequality represents the shaded region in the graph: [Image of a graph with a shaded region]?

Accepted Answer

y > -x + 2

Answer

y < -x + 2

Answer

y > x + 2

Answer

y < x + 2

Question 35

Find the solution set to the system of inequalities: x + y ≤ 4 and x - y ≥ 2

Accepted Answer

The region bounded by the lines x + y = 4 and x - y = 2, including the lines themselves

Answer

All points above the line x - y = 2

Answer

All points below the line x + y = 4

Question 36

A company manufactures two types of toys, A and B. Toy A requires 2 hours of labor and 1 unit of material, while Toy B requires 1 hour of labor and 2 units of material. If the company has 10 hours of labor and 8 units of material, how many of each type of toy should they manufacture to maximize their production?

Accepted Answer

4 of Toy A and 2 of Toy B

Answer

3 of Toy A and 3 of Toy B

Answer

5 of Toy A and 1 of Toy B

Answer

2 of Toy A and 4 of Toy B

Question 37

Which method would be most efficient for solving the system of equations: 3x + 2y = 7 and 5x - 2y = 1?

Accepted Answer

Elimination method

Answer

Substitution method

Answer

Matrix method

Answer

Graphing method

Question 38

Solve the system of equations: x = 2y and 3x - 4y = 10

Accepted Answer

(4, 2)

Answer

(10, 5)

Answer

(2, 4)

Question 39

A system of equations is considered inconsistent if...

Accepted Answer

The lines represented by the equations are parallel

Answer

The lines coincide

Answer

The lines intersect at one point

Question 40

Which of the following systems of equations has no solutions?

Accepted Answer

2x + 3y = 6, x = -3y + 2

Answer

4x + 5y = 20, 2x + y = 5

Answer

x + 2y = 5, 2x + 4y = 10

Answer

3x - y = 7, 6x - 2y = 14

Question 41

Solve the following system of equations using substitution: x + y = 5, x - y = 1.

Accepted Answer

(3, 2)

Answer

(2, 3)

Answer

(4, 1)

Answer

(1, 4)

Question 42

Solve the following system of equations using elimination: 2x + 3y = 7, x - y = 1.

Accepted Answer

(2, 1)

Answer

(2, 3)

Answer

(1, 2)

Answer

(3, 2)

Question 43

Graph the following system of inequalities: y > x + 1, y < -x + 3.

Accepted Answer

Image of the shaded region between two lines

Answer

Image of the shaded region above two lines

Answer

Image of the shaded region below two lines

Answer

Image of the shaded region outside of two lines

Question 44

Find the solution set of the following system of inequalities: x + 2y > 4, y < 3.

Accepted Answer

{(x, y) | x + 2y > 4, y < 3}

Answer

{(x, y) | x + 2y < 4, y < 3}

Answer

{(x, y) | x + 2y > 4, y = 3}

Answer

{(x, y) | x + 2y < 4, y > 3}

Question 45

Which of the following is equivalent to the inequality 3x - 2y < 6?

Accepted Answer

y > 1.5x - 3

Answer

y < 1.5x + 3

Answer

y > 3 - 1.5x

Question 46

Find the number of solutions to the following system of equations: x^2 + y^2 = 16, x + y = 4.

Accepted Answer

2

Answer

3

Answer

4

Answer

1

Question 47

Determine if the point (2, -1) is a solution to the following system of inequalities: 2x - y > 3, x + y < 1.

Accepted Answer

No

Answer

Yes

Answer

Only if x = 2

Answer

Cannot be determined

Question 48

Which of the following methods can be used to solve the system of equations 2x + y = 5 and x - y = 1?

Accepted Answer

Substitution or elimination

Answer

Graphing only

Answer

Using a matrix

Answer

Trial and error

Question 49

Find the x-intercept and y-intercept of the line represented by the equation 2x - 3y = 6.

Accepted Answer

x-intercept: 3, y-intercept: -2

Answer

x-intercept: 2, y-intercept: 3

Answer

x-intercept: -3, y-intercept: 2