Master Systems of Equations: Online Quizzes and Practice

Question 1

Which of the following methods is NOT used for solving systems of equations in two variables?

Accepted Answer

Cross-multiplication

Answer

Substitution

Answer

Elimination

Answer

Graphing

Question 2

Graphing is a useful method when the equations are linear. Which of the following equations is NOT linear?

Accepted Answer

x^2 + y^2 = 4

Answer

y = 2x + 1

Answer

y - 3 = 0

Answer

2x - 5y = 10

Question 3

A system of equations has no solution when the lines represented by the equations are:

Accepted Answer

Parallel

Answer

Intersecting

Answer

Perpendicular

Answer

Coincident

Question 4

What is the term used to describe a system of equations that has no solutions?

Accepted Answer

Inconsistent

Answer

Consistent

Answer

Dependent

Answer

Independent

Question 5

When using the elimination method to solve a system of equations, what operation is performed to eliminate a variable?

Accepted Answer

Adding or subtracting the equations

Answer

Multiplying both equations by the same constant

Answer

Graphing the equations

Answer

Substituting one variable with an equivalent expression

Question 6

In the graphing method for solving systems of equations, which step is NOT involved?

Accepted Answer

Solving the system algebraically

Answer

Plotting the intercepts

Answer

Connecting the intercepts

Answer

Finding the intersection point

Question 7

What is the characteristic of a dependent system of equations?

Accepted Answer

It has infinitely many solutions

Answer

It has a unique solution

Answer

It has no solutions

Answer

Its equations are parallel

Question 8

A farmer has 120 feet of fencing to enclose a rectangular plot of land. If the length of the plot is 20 feet more than its width, what is the width of the plot?

Accepted Answer

30 feet

Answer

25 feet

Answer

35 feet

Answer

40 feet

Question 9

If the system of equations 3x + 2y = 12 and 2x - y = 5 has no solution, what conclusion can be drawn about the lines represented by the equations?

Accepted Answer

They are parallel lines.

Answer

They intersect at one point.

Answer

They coincide.

Answer

They are perpendicular lines.

Question 10

Solve the system of equations using elimination: x + 2y = 7 and 3x - y = 4.

Accepted Answer

(2, 1.5)

Answer

(1.5, 2)

Answer

(2.5, 1)

Answer

(1, 2.5)

Question 11

Which of the following systems of equations represents a pair of perpendicular lines?

Accepted Answer

x + y = 0 and y = x + 2

Answer

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

Answer

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

Answer

3x + y = 4 and x = y - 1

Question 12

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

Accepted Answer

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

Answer

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

Answer

3x + y = 5 and x + 3y = 9

Answer

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

Question 13

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

Accepted Answer

Matrix multiplication

Answer

Substitution

Answer

Elimination

Answer

Graphing

Question 14

Consider the system of equations: x + y = 5, x - y = 1. What is the value of x?

Accepted Answer

3

Answer

2

Answer

4

Answer

The provided system has no solution.

Question 15

Consider the following system of equations, graphed on the coordinate plane: y = 2x - 1, y = -x + 3. What is the solution to the system?

Accepted Answer

(1, 1)

Answer

(0, -1)

Answer

(-1, -3)

Answer

The system has infinitely many solutions.

Question 16

Which of the following is the slope-intercept form of the equation y = 3x - 2?

Accepted Answer

y = 3x - 2

Answer

y = -2x + 3

Answer

y - 2 = 3x

Answer

x - 2 = 3y

Question 17

In the substitution method for solving systems of equations, what do you do to eliminate one variable?

Accepted Answer

Replace it with an equivalent expression from the other equation

Answer

Combine it with the other variable

Answer

Graph the equations

Question 18

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

Accepted Answer

(2, 3)

Answer

(3, 2)

Answer

(4, 1)

Question 19

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

Accepted Answer

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

Answer

y = x + 1 and y = 2x + 1

Answer

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

Question 20

In the elimination method of solving systems of equations, what is the first step?

Accepted Answer

Multiply both equations by the same number to make coefficients of one variable opposite

Answer

Subtract one equation from the other

Answer

Add the two equations together

Answer

Multiply one equation by the reciprocal of the coefficient of one of the variables

Question 21

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

Accepted Answer

Infinite solutions

Answer

Consistent and independent

Answer

Consistent and dependent

Answer

Inconsistent

Question 22

What is the solution to the system of equations: x + y = 5 and 2x - y = 1?

Accepted Answer

(2, 3)

Answer

(3, 2)

Answer

(-2, 3)

Answer

(-3, 2)

Question 23

Rewritten: Graph the following system of equations and identify the solution: y = 2x + 1 and y = x - 1

Accepted Answer

Solution: (1, 0)

Answer

Solution: (-1, -2)

Answer

Solution: (0, -1)

Answer

The lines are parallel, no solution

Question 24

What does it mean when a system of equations has no solution?

Accepted Answer

The lines are parallel.

Answer

The lines intersect at one point.

Answer

The lines are perpendicular.

Answer

The lines coincide.

Question 25

Find the slope of the line represented by the equation: 2y - 4x = 8.

Accepted Answer

-2

Answer

2

Answer

1/2

Answer

-1/2

Question 26

Graphically represent the system of equations: y = 2x + 1, y = -x + 3

Accepted Answer

The lines intersect at (1, 3).

Answer

The lines are perpendicular.

Answer

The lines are parallel.

Answer

The lines coincide.

Question 27

Which method should be used to solve the system of equations: x^2 + y^2 = 25, y = 2x?

Accepted Answer

Substitution

Answer

Elimination

Answer

Cramer's Rule

Answer

Graphing

Question 28

Determine the number of solutions to the system of equations: 3x + 2y = 6, 6x + 4y = 12

Accepted Answer

Infinitely many

Answer

One

Answer

Two

Answer

None

Question 29

Determine whether the following system of equations is consistent or inconsistent: 2x + y = 3, 4x + 2y = 6

Accepted Answer

Consistent

Answer

Dependent

Answer

Inconsistent

Answer

Underdetermined

Question 30

Application Problem: A farmer has 200 feet of fencing to enclose a rectangular plot of land. If the length of the plot is twice its width, find the dimensions of the plot that will enclose the maximum area.

Accepted Answer

Length: 66.67 feet, Width: 33.33 feet

Answer

Length: 50 feet, Width: 25 feet

Answer

Length: 40 feet, Width: 20 feet

Question 31

Determine whether the system of equations is consistent or inconsistent: x + 3y = 6, 2x + 6y = 12

Accepted Answer

Consistent

Answer

Underdetermined

Answer

Dependent

Answer

Inconsistent

Question 32

Which of the following systems of equations represents a line that is perpendicular to the x-axis?

Accepted Answer

y = 4, x + 2 = 0

Answer

2x - y = 5, x - 2y = 0

Answer

y = 3x + 1, x + y = 3

Answer

x + y = 1, 2x + 2y = 2

Question 33

A coffee shop sells two types of coffee beans: Arabica and Robusta. Arabica costs $12 per pound, and Robusta costs $8 per pound. If a customer buys a mixture of 5 pounds of coffee beans for a total of $48, how many pounds of Arabica beans did they buy?

Accepted Answer

3

Answer

4

Answer

2

Question 34

A system of equations has no solution. What does this imply about the lines represented by the equations?

Accepted Answer

The lines are parallel.

Answer

The lines intersect at one point.

Answer

The lines coincide.

Question 35

The price of 3 apples and 2 oranges is $4. The price of 2 apples and 3 oranges is $3.50. What is the cost of one apple?

Accepted Answer

$0.75

Answer

$1.00

Answer

$0.50

Question 36

If a system of equations has infinitely many solutions, what can we conclude about the slopes and y-intercepts of the lines represented by the equations?

Accepted Answer

The lines have the same slope and the same y-intercept.

Answer

The lines have different slopes but the same y-intercept.

Question 37

A system of equations is said to be inconsistent if:

Accepted Answer

It has no solution.

Answer

It has multiple solutions.

Answer

It has one unique solution.

Question 38

A system of equations has an infinite number of solutions. What does this indicate?

Accepted Answer

The equations represent the same line.

Answer

There is only one possible solution.

Answer

There are no possible solutions.

Question 39

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

Accepted Answer

-3

Answer

-2

Answer

3

Question 40

Which of the following systems of equations represents a system of three variables?

Accepted Answer

2x + 3y - 4z = 5, x - y + 2z = 1, and 3x + 2y - z = 0

Answer

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

Answer

3x - 2y = 6 and 4x + 6y = 12

Question 41

A movie theater sells adult tickets for $12 and student tickets for $8.  On a particular day, the theater sold 200 tickets and made $1840 in total revenue.  Which system of equations represents this situation, where *a* is the number of adult tickets and *s* is the number of student tickets sold?

Accepted Answer

a + s = 200; 12a + 8s = 1840

Answer

12a + 8s = 200; a + s = 1840

Answer

a + s = 1840; 12a + 8s = 200

Answer

a - s = 200; 12a + 8s = 1840

Question 42

Solve the following system of equations using the substitution method:

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

Accepted Answer

x = 3, y = 4

Answer

x = -3, y = 1

Answer

x = 5, y = 0

Answer

x = 2, y = 3

Question 43

Solve for *y* in the system of equations using the elimination method:

2x + 5y = 17
4x - 3y = 1

Accepted Answer

y = 3

Answer

y = -2

Answer

y = -3

Answer

y = 2

Question 44

Which graph represents the solution to the system of inequalities?

y > x + 2
y ≤ -2x + 1

Accepted Answer

A graph with a dashed line shaded above for y > x + 2 and a solid line shaded below for y ≤ -2x + 1. The solution area is the overlapping shaded region.

Answer

A graph where both lines are solid and the shaded area is above both lines.

Answer

A graph with a solid line shaded below for y > x + 2 and a dashed line shaded above for y ≤ -2x + 1.

Answer

A graph where the shaded areas for both inequalities do not overlap.

Question 45

The lines represented by the equations 2x + 3y = 12 and 4x + 6y = 24 are:

Accepted Answer

The same line

Answer

Perpendicular lines

Answer

Intersecting lines that are not perpendicular

Answer

Parallel lines

Question 46

A system of equations has no solution. What does this tell us about the graphs of the equations?

Accepted Answer

The lines are parallel.

Answer

The lines intersect at one point.

Answer

The lines are the same.

Answer

The lines are perpendicular.

Question 47

A restaurant sells vegetarian pizzas for $12 each and pepperoni pizzas for $15 each.  A customer bought 8 pizzas in total and spent $102.  How many of each type of pizza did they buy?

Accepted Answer

2 vegetarian pizzas and 6 pepperoni pizzas

Answer

3 vegetarian pizzas and 5 pepperoni pizzas

Answer

5 vegetarian pizzas and 3 pepperoni pizzas

Answer

4 vegetarian pizzas and 4 pepperoni pizzas

Question 48

What is the point of intersection of the lines represented by the equations y = 3x - 1 and y = -x + 5?

Accepted Answer

(1.5, 3.5)

Answer

(0, 4)

Answer

(1, 2)

Answer

(2, 5)

Question 49

Consider the system of inequalities:

y ≥ -2x + 3
y < x - 1
Which point is a solution to this system?

Accepted Answer

(3, 1)

Answer

(2, 3)

Answer

(0, 0)

Answer

(1, -1)

Question 50

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

Accepted Answer

All of the above

Answer

Graphing only

Answer

Substitution only

Answer

Elimination only