Master Systems of Equations: Online Quizzes and Practice

Question 1

In the substitution method of solving systems of equations, what do we substitute?

Accepted Answer

One variable into another equation

Answer

One equation into another equation

Answer

One value into another variable

Question 2

Which of the following statements best describes the elimination method of solving systems of equations?

Accepted Answer

Add or subtract equations to eliminate one variable

Answer

Multiply equations to eliminate one variable

Answer

Substitute one variable from one equation into another equation

Question 3

Which system of equations has an infinite number of solutions?

Accepted Answer

x + y = 5 and 2x + 2y = 10

Answer

3x - y = 6 and x + 2y = 12

Answer

2x + 3y = 8 and 4x + 6y = 16

Question 4

Which of the following methods is not used for graphing a system of equations?

Accepted Answer

Substituting values for one variable and solving for the other

Answer

Plotting the lines and finding their intersection

Answer

Using a graphing calculator

Question 5

Which of the following is an example of a system of equations in three variables?

Accepted Answer

x + y = 5, 2x - z = 1, and y + z = 3

Answer

x + y = 5 and 2x + y = 7

Answer

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

Question 6

In solving a system of equations in three variables using elimination, what do we add or subtract?

Accepted Answer

Equations

Answer

Variables

Answer

Values

Question 7

Eliminate the variable x from the system: 2x + 3y = 7, x - y = 5

Accepted Answer

5y = 2

Answer

y = 2

Answer

x = 5 + y

Answer

2y = 1

Question 8

Which of the following systems of equations has no solution?

Accepted Answer

x + y = 2, x + y = 3

Answer

x - y = 5, 2x-2y = 10

Answer

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

Answer

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

Question 9

Which of the following is a system of linear equations?

Accepted Answer

y = 2x + 1

Answer

x^2 + y^2 = 4

Answer

x + |y| = 5

Answer

|x - y| = 3

Question 10

Which of the following is NOT a valid method for solving systems of equations?

Accepted Answer

Guess and check

Answer

Graphing

Answer

Substitution

Answer

Elimination

Question 11

Consider the system of equations: 2x + y = 5, 3x - 2y = 1. Which of the following methods can be used to solve this system?

Accepted Answer

Any of the above

Answer

Graphing only

Answer

Substitution only

Answer

Elimination only

Question 12

Which of the following situations cannot be represented by a system of equations?

Accepted Answer

The height of a ball thrown into the air at a specific angle

Answer

The total cost of buying apples and oranges

Answer

The distance traveled by a car at a constant speed

Answer

The relationship between the number of people and the amount of food needed

Question 13

Determine if the point (2, 5) is a solution to the system of equations: 
y = x + 3
2x - y = 1

Accepted Answer

Yes

Answer

No

Question 14

Which of the following is NOT a valid method for solving systems of equations?

Accepted Answer

Factoring

Answer

Graphing

Answer

Substitution

Answer

Elimination

Question 15

What is the outcome of eliminating x from the system: x + 2y = 7, 3x - y = 1?

Accepted Answer

5y = 16

Answer

y = 3

Answer

x = 2

Answer

3y = 17

Question 16

Which characteristic describes a consistent system of equations?

Accepted Answer

The corresponding lines intersect at exactly one point

Answer

The corresponding lines are parallel and have no intersection

Answer

The corresponding lines overlap and have infinitely many intersections

Answer

The system has no solution

Question 17

Determine the number of solutions for the system: y = 2x + 1, y = -x + 3.

Accepted Answer

Infinitely many

Answer

One

Answer

Two

Answer

No solution

Question 18

Find the slope of the line represented by the equation 2x + 3y = 6.

Accepted Answer

2/3

Answer

-2/3

Answer

3/2

Answer

-3/2

Question 19

Which of the following systems of equations represents parallel lines?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 20

Find the system of equations that represents the given graph. Lines are shown as y = 2x - 1 and y = -x + 3:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 21

Solve the system of equations using elimination:
x - y = 2
2x + y = 5

Accepted Answer

x = 3, y = 1

Answer

x = 2, y = 0

Answer

x = 4, y = 2

Answer

x = 1, y = 3

Question 22

Use the substitution method to solve the following system: x - y = 3, x + 2y = 11.

Accepted Answer

(2, 5)

Answer

(5, 2)

Answer

(-2, -5)

Answer

(-5, -2)

Question 23

For which system is substitution unsuitable:

Accepted Answer

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

Answer

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

Answer

3x + 2y = 7, 5x - y = 10

Answer

4x - 3y = 12, x + 2y = 5

Question 24

Two numbers sum to 20. Their difference is 6. Find the numbers.

Accepted Answer

(7, 13)

Answer

(13, 7)

Answer

(8, 12)

Answer

(12, 8)

Question 25

In a system of equations, how does multiplying an equation by a non-zero constant affect the solution?

Accepted Answer

It remains the same

Answer

It changes

Answer

The system becomes inconsistent

Answer

The system becomes dependent

Question 26

Which of the following represents a system of linear equations in three variables?

Accepted Answer

2x + 3y + 4z = 5, x - 2y + z = 3, 3x + y - z = 7

Answer

x^2 + y^2 = 1, x - y = 0

Answer

x + y = 2, x - y = 4

Answer

2x + 3y = 5, 4x + 6y = 10

Question 27

Which of the following methods is NOT used to solve systems of linear equations?

Accepted Answer

Division

Answer

Elimination

Answer

Substitution

Answer

Graphing

Question 28

Which of the following is the correct procedure for the elimination method?

Accepted Answer

Add or subtract the equations to eliminate one variable.

Answer

Substitute one equation into the other and solve for the remaining variable.

Answer

Multiply both equations by the same number to make one variable a multiple of the other.

Question 29

Find the solution to the system of equations: 2x - 3y = 1, x + y = 4

Accepted Answer

x = 3, y = 1

Answer

x = -1, y = -3

Answer

x = 2, y = 2

Answer

x = 1, y = 3

Question 30

Which of the following systems of equations has no solution?

Accepted Answer

x + y = 2, x + y = 3

Answer

x - y = 2, x + y = 4

Answer

x + y = 2, x - y = 0

Question 31

Provide an example of a real-life application of systems of linear equations.

Accepted Answer

Mixing different solutions with varying concentrations to achieve a desired concentration

Answer

Finding the slope of a line

Answer

Calculating the area of a triangle

Question 32

When graphed, what does the system of equations y = 2x + 1 and y = x - 1 look like?

Accepted Answer

Two intersecting lines

Answer

One line

Answer

Two parallel lines

Answer

Two perpendicular lines

Question 33

What is the solution to the system of equations: x + y = 10 and 2x - y = 5?

Accepted Answer

(x = 5, y = 5)

Answer

(x = 5, y = 0)

Answer

(x = 10, y = 0)

Answer

(x = 0, y = 10)

Question 34

Which of the following is NOT a common method for solving systems of equations?

Accepted Answer

Addition

Answer

Substitution

Answer

Graphing

Answer

Elimination

Question 35

What is the solution to the system of equations x = 2 and y = 3?

Accepted Answer

(2, 3)

Answer

(1, 1)

Answer

(3, 2)

Answer

(0, 0)

Question 36

What is the shape of the shaded region representing the solution to the system of inequalities: x + y ≤ 5 and x - y ≥ 1?

Accepted Answer

Quadrilateral

Answer

Circle

Answer

Square

Answer

Triangle

Question 37

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

Accepted Answer

Substitution

Answer

Elimination

Answer

Graphing

Question 38

If the system of equations: ax + by = c and dx + ey = f has infinitely many solutions, what characteristic must the coefficients satisfy?

Accepted Answer

The coefficients are proportional.

Answer

The coefficients are equal.

Answer

The coefficients are reciprocals.

Question 39

Which of the following systems of equations has infinitely many solutions?

Accepted Answer

(x + y = 0, 2x + 2y = 0)

Answer

(2x + y = 0, 2x + y = 4)

Answer

(x + y = 0, 2x + y = 0)

Question 40

Use the substitution method to solve the system of equations: x - y = 3, 2x + y = 7

Accepted Answer

(x = 5, y = 2)

Answer

(x = 2, y = -1)

Answer

(x = 4, y = 1)

Question 41

Use elimination method to solve the system of equations: 3x + 2y = 11, x - y = 1

Accepted Answer

(x = 3, y = 2)

Answer

(x = 0, y = 5)

Answer

(x = 2, y = 3)

Question 42

Which graph represents the system of equations: y = 2x - 3, y = -x + 1?

Accepted Answer

Two intersecting lines

Answer

Two parallel lines

Answer

One line

Question 43

Solve the system of equations: x + y + z = 6, x - y + z = 2, -x + y + z = 4

Accepted Answer

(x = 2, y = 1, z = 3)

Answer

(x = 1, y = 2, z = 3)

Answer

(x = 2, y = 3, z = 1)

Question 44

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

Accepted Answer

(y = x^2, x + y = 5)

Answer

(2x + 3y = 7, y = 2x - 1)

Answer

(x + y = 5, x - y = 3)

Question 45

Provide an example of a real-world application of solving systems of equations.

Accepted Answer

Determining the concentration of a solution by mixing chemicals in different proportions

Answer

Finding the distance between two points on a map

Question 46

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

Accepted Answer

All of the above

Answer

Elimination

Answer

Substitution

Answer

Graphing

Question 47

Which of the following is not a type of system of equations?

Accepted Answer

Homogeneous system

Answer

Consistent system

Answer

Dependent system

Answer

Inconsistent system

Question 48

Which of the following is a characteristic of an inconsistent system of equations?

Accepted Answer

The graphs of the equations do not intersect.

Answer

The graphs of the equations intersect at one point.

Answer

The graphs of the equations are perpendicular.

Answer

The graphs of the equations are parallel.