Systems of Equations and Inequalities: Master the Concepts with Engaging Quizzes

Question 1

What is the solution to the inequality:
2x - 3y > 6?

Accepted Answer

x > 3y - 3

Answer

x < 3y - 3

Answer

y > 2x - 3

Answer

y < 2x - 3

Question 2

What is the equation of the line with a slope of -2 and a y-intercept of 3?

Accepted Answer

y = -2x + 3

Answer

y = 2x + 3

Answer

y = -2x - 3

Answer

y = 2x - 3

Question 3

Solve the following system of inequalities: x > 0, y ≤ 2

Accepted Answer

x > 0, y ≤ 2

Answer

x ≥ 0, y > 2

Answer

x ≥ 0, y < 2

Answer

x < 0, y > 2

Question 4

Which of the following is an equivalent system of equations to x + y = 5 and 2x - y = 1?

Accepted Answer

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

Answer

x + y = 5, 2x + y = 7

Answer

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

Answer

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

Question 5

Which of the following is a step in the substitution method for solving systems of equations?

Accepted Answer

Substitute one equation into the other

Answer

Add the two equations together

Answer

Multiply one equation by a number

Answer

Graph the two equations

Question 6

Which of the following represents a system of equations?

Accepted Answer

The equations x + y = 5 and 2x - 3y = 10

Answer

The equation x + y = 5

Answer

The equation x = y

Answer

The inequality y > 2

Question 7

Solve the following system of equations graphically: x + y = 3, x - y = 1

Accepted Answer

(1, 1)

Answer

(2, 1)

Answer

(1, 2)

Answer

(2, 2)

Question 8

Which of the following represents a system of inequalities?

Accepted Answer

The inequalities x + y < 5 and 2x - 3y > 10

Answer

The inequality x + y < 5

Answer

The equation x = 2

Answer

The equation y = -1

Question 9

Which of the following is a solution to the system of inequalities x > 2 and y < -1?

Accepted Answer

(3, -2)

Answer

(2, -3)

Answer

(-3, 2)

Answer

(-2, 3)

Question 10

Which algebraic method can be used to solve systems of equations?

Accepted Answer

Substituting one equation into the other and solving for a variable

Answer

Graphing the equations and finding the intersection point

Answer

Creating a table of values to find the intersection point

Answer

Using a graphing calculator to find the intersection point

Question 11

Which of the following represents the solution to the system of equations 2x + 3y = 11 and x - y = 1?

Accepted Answer

(2, 3)

Answer

(3, 2)

Answer

(4, 1)

Answer

(1, 4)

Question 12

Solve the system of inequalities graphically and select the shaded region that satisfies both inequalities:

x + y > 5
y < 2x + 1

Accepted Answer

Below y = 2x + 1 and right of x + y = 5

Answer

Above y = 2x + 1 and left of x + y = 5

Answer

Below y = 2x + 1 and left of x + y = 5

Answer

Above y = 2x + 1 and right of x + y = 5

Question 13

Graphically, how do you determine if two lines are parallel?

Accepted Answer

The lines have the same slope

Answer

The lines have different slopes

Answer

The lines have the same y-intercept

Answer

The lines have the same x-intercept

Question 14

Which of the following is a linear inequality?

Accepted Answer

x > 2

Answer

x² + y² > 4

Answer

x < 2 or x > 3

Answer

y = x + 1

Question 15

Which of the following represents the solution region of the inequality: -2x + y ≤ 4?

Accepted Answer

Points below the line y = 2x - 4

Answer

Points above the line y = -2x + 4

Answer

Points on the line y = 2x - 4

Answer

The origin

Question 16

Which of the following systems of equations has no solution?

Accepted Answer

x + y = 2 and x + y = 3

Answer

2x + y = 4 and x - y = 2

Answer

x - y = 1 and x + y = 5

Answer

x + 2y = 6 and 2x + 4y = 12

Question 17

Solve the following system of linear equations graphically: 2x + y = 4
x - y = 1

Accepted Answer

(1, 1)

Answer

(2, 0)

Answer

(0, 4)

Answer

(4, 0)

Question 18

Which of the following inequalities represents the shaded region in the given graph?

Accepted Answer

y ≤ 2x + 1

Answer

y ≥ 2x + 1

Answer

y < 2x + 1

Answer

y > 2x + 1

Question 19

Solve the following inequality algebraically: 2x + 3 > 5

Accepted Answer

x > 1

Answer

x < 1

Answer

x ≥ 1

Answer

x ≤ 1

Question 20

Solve the system of equations: 
2x + 3y = 13
x - y = 1

Accepted Answer

(3, 2)

Answer

(2, 3)

Answer

(1, 4)

Answer

(-1, 6)

Question 21

Find the slope of the line represented by the equation: 
y = -2x + 5

Accepted Answer

-2

Answer

2

Answer

1/2

Answer

-1/2

Question 22

Which of the following inequalities represents the shaded region below the line y = 2x + 1?

Accepted Answer

y < 2x + 1

Answer

y > 2x + 1

Answer

y ≥ 2x + 1

Answer

y ≤ 2x + 1

Question 23

Which of the following is the graphical representation of the system of equations: y = 2x + 1 and y = -x + 5?

Accepted Answer

Two intersecting lines

Answer

A parabola and a line

Answer

Parallel lines

Answer

A circle and a line

Question 24

Find the solution region of the following system of inequalities: x + y ≤ 5, x ≥ 1, and y ≥ 0

Accepted Answer

{(x, y) | x ≥ 1, y ≥ 0, and x + y ≤ 5}

Answer

{(x, y) | x ≤ 1, y ≥ 0, and x + y > 5}

Answer

{(x, y) | x ≤ 1, y ≤ 0, and x + y ≤ 5}

Answer

{(x, y) | x ≥ 1, y ≤ 0, and x + y ≤ 5}

Question 25

Identify the linear system among the following equations:

Accepted Answer

2x + 3y = 6 and y = -x + 5

Answer

e^x + ln y = 2 and x + y = 3

Answer

sin x + cos y = 1 and x + y = 0

Answer

x^2 + y^2 = 4 and x - y = 1

Question 26

Which of the following is an example of a system of equations?

Accepted Answer

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

Answer

y = 2x^2 + 1

Answer

y > 2x - 1

Answer

x = 5

Question 27

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

Accepted Answer

x = 2, y = 1

Answer

x = 1, y = 2

Answer

x = 2, y = 2

Question 28

Which of the following is an example of an inconsistent system of equations?

Accepted Answer

2x + y = 5, 2x + y = 7

Answer

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

Answer

2x + y = 5, 2y = 10

Answer

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

Question 29

Which of the following methods can be used to solve systems of equations?

Accepted Answer

Substitution, Elimination, Graphing

Answer

Integration, Differentiation, Logarithms

Answer

Trigonometry, Calculus, Matrices

Answer

Factoring, Completing the Square, Quadratic Formula

Question 30

Which of the following equations represents a line parallel to the x-axis?

Accepted Answer

y = 2

Answer

y = 2x + 1

Answer

y = x + 2

Answer

y = -x + 2

Question 31

Which of the following equations represents a line perpendicular to the line y = 2x + 1?

Accepted Answer

y = -1/2x + 2

Answer

y = -2x + 1

Answer

y = x + 2

Answer

y = 2x - 1

Question 32

Which of the following is a system of equations?

Accepted Answer

2x + 3y = 7
y - 2x = 5

Answer

x = 5

Answer

x + y ≥ 10

Answer

y = mx + c

Question 33

Find the solution to the system of equations: 2x + y = 7, x - 2y = 5

Accepted Answer

x = 2, y = 3

Answer

x = -3, y = -2

Answer

x = -2, y = -3

Answer

x = 3, y = 2

Question 34

What is the solution to the inequality: 2x - 5 > 1?

Accepted Answer

x > 3

Answer

x > -3

Answer

x < 3

Answer

x < -3

Question 35

Graphically, the solution to the inequality x + y ≤ 4 is represented by:

Accepted Answer

The shaded region below the line x + y = 4.

Answer

The line x + y = 4.

Answer

The shaded region above the line x + y = 4.

Answer

The entire coordinate plane.

Question 36

Which of the following systems of inequalities has no solution?

Accepted Answer

y ≥ 2x + 1, y ≤ -x + 1

Answer

y > x + 1, y ≤ x + 3

Answer

y < x - 1, y ≥ x - 3

Answer

y ≥ 2x + 1, y ≤ 2x + 3

Question 37

Which of the following is an application of systems of equations?

Accepted Answer

Finding the point of intersection of two lines.

Answer

Solving quadratic equations.

Answer

Finding the area of a circle.

Answer

Solving exponential equations.

Question 38

The system of equations x + y = 7 and x - y = 3 can be used to determine:

Accepted Answer

The values of both x and y.

Answer

The value of x only.

Answer

The area of a rectangle.

Answer

The value of y only.

Question 39

Which of the following is a characteristic of a system of linear equations?

Accepted Answer

It can be represented graphically as a set of intersecting lines.

Answer

It always has exactly one solution.

Answer

It is always nonlinear.

Question 40

The graph of the system of inequalities y ≥ x + 1 and y ≤ -x + 3 represents:

Accepted Answer

The region shaded by both lines.

Answer

The region below both lines.

Answer

The region above both lines.

Answer

The region outside both lines.

Question 41

A movie theater sells adult tickets for $10 and student tickets for $8. On one evening, they sold 250 tickets and made a total of $2200. Let 'a' represent the number of adult tickets and 's' represent the number of student tickets. Which system of equations could be used to find the number of adult and student tickets sold?

Accepted Answer

a + s = 250; 10a + 8s = 2200

Answer

a + s = 2200; 10a + 8s = 250

Answer

a - s = 250; 10a + 8s = 2200

Answer

10a + 8s = 250; a + s = 2200

Question 42

Find the solution to the system of equations by graphing:

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

Accepted Answer

(1, 2)

Answer

(2, 1)

Answer

(-1, 0)

Answer

(0, 4)

Question 43

Which of the following systems of equations has no solution?

Accepted Answer

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

Answer

x + y = 5
x - y = 1

Answer

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

Answer

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

Question 44

A bakery sells cookies for $1.50 each and brownies for $2.00 each.  They want to make at least $50 from selling cookies and brownies. Let 'x' represent the number of cookies and 'y' represent the number of brownies. Which inequality represents this situation?

Accepted Answer

1.5x + 2y ≥ 50

Answer

1.5x + 2y > 50

Answer

1.5x + 2y < 50

Answer

1.5x + 2y ≤ 50

Question 45

A farmer wants to plant corn and soybeans on his farm. He has a maximum of 100 acres available for planting.  He wants to plant at least 20 acres of corn and at least 30 acres of soybeans. Let 'c' represent the number of acres of corn and 's' represent the number of acres of soybeans. Which system of inequalities represents the constraints on the number of acres he can plant?

Accepted Answer

c + s ≤ 100; c ≥ 20; s ≥ 30

Answer

c + s ≥ 100; c ≤ 20; s ≤ 30

Answer

c + s ≥ 100; c ≥ 20; s ≥ 30

Answer

c + s ≤ 100; c ≤ 20; s ≤ 30

Question 46

Which inequality represents the shaded region in the graph of y > x + 2?

Accepted Answer

y > x + 2

Answer

x > y + 2

Answer

y < x + 2

Answer

x < y + 2

Question 47

What is the slope of the line that passes through the points (2, 3) and (4, 7)?

Accepted Answer

2

Answer

-1

Answer

1

Answer

-2

Question 48

Which of the following systems of equations has no solution?

Accepted Answer

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

Answer

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

Answer

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

Answer

y = x + 2 and y = 2x + 4

Question 49

What is the y-intercept of the line represented by the equation y = 3x - 2?

Accepted Answer

-2

Answer

3

Answer

-3

Answer

2

Question 50

What is the x-intercept of the line represented by the equation y = 2x + 6?

Accepted Answer

-3

Answer

3

Answer

2

Answer

-2

Question 51

Which of the following equations represents a vertical line passing through the point (3, -2)?

Accepted Answer

x = 3

Answer

x = -2

Answer

y = -2

Answer

y = 3

Question 52

Which of the following equations represents a horizontal line passing through the point (-1, 4)?

Accepted Answer

y = 4

Answer

y = -1

Answer

x = -1

Answer

x = 4

Question 53

Which of the following is the solution to the system of inequalities y > x + 2 and y < 2x - 1?

Accepted Answer

The shaded region above the line y = x + 2 and below the line y = 2x - 1.

Answer

The shaded region below the line y = x + 2 and above the line y = 2x - 1.

Answer

The shaded region to the left of the line y = x + 2 and to the right of the line y = 2x - 1.