Solving Linear Equations: Master the Basics with Interactive Quizzes

Question 1

Solve for y using substitution method, given 2y + 3x = 6 and x = 1

Accepted Answer

y = 2

Answer

y = 1.5

Answer

y = 2.5

Answer

y = 3

Question 2

Solve for x in the equation: |x - 5| = 3

Accepted Answer

x = 2 or x = 8

Answer

x = 3 or x = 8

Answer

x = 2 or x = 7

Answer

x = 3 or x = 7

Question 3

Translate the following verbal inequality into a mathematical inequality: The sum of two numbers is less than 15

Accepted Answer

x + y < 15

Answer

x + y > 15

Answer

x - y > 15

Answer

x - y < 15

Question 4

Solve the linear inequality: 2x - 5 > 11

Accepted Answer

x > 6

Answer

x < 6

Answer

x > 8

Answer

x < 8

Question 5

Solve for z in the equation 3(z + 2) = 21.

Accepted Answer

z = 7

Answer

z = 3

Answer

z = 5

Answer

z = 9

Question 6

Solve for x in the equation |x - 3| = 5.

Accepted Answer

x = 8 or x = -2

Answer

x = 5 or x = -1

Answer

x = 3 or x = -5

Answer

No solution

Question 7

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

Accepted Answer

Using a calculator

Answer

Substitution

Answer

Elimination

Answer

Graphing

Question 8

What is the y-intercept of the line represented by the equation: y = -2x + 5?

Accepted Answer

5

Answer

-2

Answer

2

Answer

-5

Question 9

What is NOT a characteristic of a linear equation?

Accepted Answer

Constant second difference

Answer

Constant slope

Answer

Constant y-intercept

Answer

Constant rate of change

Question 10

Which of the following is the graph of the equation y = 2x + 1?

Accepted Answer

A line with a slope of 2 and a y-intercept of 1

Answer

A line with a slope of 1 and a y-intercept of 2

Answer

A parabola with a vertex at (1, 2)

Answer

A circle with a radius of 1

Question 11

Which of the following is a rational equation?

Accepted Answer

x/(x+1) = 2

Answer

x^2 - 5 = 0

Answer

sinx = 0

Answer

e^x = 10

Question 12

Solve for x in the equation: 2x + 5 = 13

Accepted Answer

x = 4

Answer

x = 5

Answer

x = 6

Answer

x = 7

Question 13

Solve for y in the equation: 3(y - 2) = 15

Accepted Answer

y = 7

Answer

y = 4

Answer

y = 5

Answer

y = 9

Question 14

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

Accepted Answer

y = 2

Answer

y = x + 1

Answer

y = -x

Answer

y = 2x - 5

Question 15

To solve the system of linear equations 2x + 3y = 12 and 4x - y = 15, which method is most efficient and accurate?

Accepted Answer

Elimination Method

Answer

Substitution Method

Answer

Graphing Method

Question 16

When solving the equation 2x + 3y = 6 using elimination, which of the following is NOT a valid step?

Accepted Answer

Add 2x to both sides

Answer

Multiply the first equation by 2

Answer

Multiply the second equation by -3

Question 17

Solve the system of linear equations: x + y = 5 and x - y = 1 using substitution

Accepted Answer

x = 3 and y = 2

Answer

x = 5 and y = 0

Answer

No solution

Answer

x = 1 and y = 4

Question 18

Find the solution to the equation: 2*(x - 3) = 8

Accepted Answer

7

Answer

11

Answer

-1

Answer

5

Question 19

A clothing store sells shirts for $15 and pants for $25. If a customer buys 3 shirts and 2 pants, how much will they spend in total?

Accepted Answer

$105

Answer

$75

Answer

$90

Question 20

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

Accepted Answer

2

Answer

-2

Answer

-5

Answer

5

Question 21

What is the *y*-intercept of the line represented by the equation: *y* = -3*x* + 1?

Accepted Answer

1

Answer

-3

Answer

3

Answer

0

Question 22

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

Accepted Answer

Guess and Check

Answer

Substitution

Answer

Graphing

Answer

Elimination

Question 23

What is the solution to the equation  *x - 8 = 12*?

Accepted Answer

x = 20

Answer

x = 25

Answer

x = 30

Answer

x = 15

Question 24

What is the value of *x* in the equation *2(x - 1) = 4*?

Accepted Answer

x = 3

Answer

x = 4

Answer

x = 2

Answer

x = 5

Question 25

Solve for *x* in the equation *x + 5 = 10*.

Accepted Answer

x = 5

Answer

x = -5

Answer

x = 10

Answer

x = 15

Question 26

The sum of two numbers is 20. One number is 5. What is the other number?

Accepted Answer

x = 15

Answer

x = 10

Answer

x = 18

Answer

x = 12

Question 27

Apples cost $0.50 each and oranges cost $0.75 each. If a customer buys 3 apples and 2 oranges, what is the total cost?

Accepted Answer

$2.75

Answer

$2.00

Answer

$3.00

Answer

$2.50

Question 28

A car travels 120 miles in 2 hours. What is the car's average speed in miles per hour?

Accepted Answer

60 mph

Answer

40 mph

Answer

100 mph

Answer

80 mph

Question 29

What is the solution to the equation *2x - 7 = 11*?

Accepted Answer

x = 9

Answer

x = -2

Answer

x = 11

Answer

x = 7

Question 30

What is the first step in solving the equation *4(x - 2) = 12*?

Accepted Answer

Distribute the 4

Answer

Add 2 to both sides

Answer

Subtract 2 from both sides

Answer

Divide both sides by 4

Question 31

Solve for x using substitution: y = 2x + 1 and 3x - y = 4

Accepted Answer

x = 5

Answer

x = 1

Answer

x = -1

Answer

x = -5

Question 32

A car rental company charges a flat fee of $25 plus $0.30 per mile driven. If a customer's bill was $56.50, how many miles did they drive?

Accepted Answer

105 miles

Answer

95 miles

Answer

75 miles

Answer

125 miles

Question 33

What is the solution to the equation 2x + 5 = 11?

Accepted Answer

x = 3

Answer

x = 2

Answer

x = -3

Answer

x = 8

Question 34

Which of the following is the correct first step to solve the equation 3x - 7 = 14?

Accepted Answer

Add 7 to both sides of the equation.

Answer

Multiply both sides of the equation by 3.

Answer

Subtract 14 from both sides of the equation.

Answer

Divide both sides of the equation by 3.

Question 35

Solve for y: 4y - 8 = 12

Accepted Answer

y = 5

Answer

y = -1

Answer

y = -5

Answer

y = 1

Question 36

What is the solution to the equation 5x + 2 = 2x - 7?

Accepted Answer

x = -3

Answer

x = 1

Answer

x = -1

Answer

x = 3

Question 37

Which of the following graphs represents the solution to the equation y = 2x - 1?

Accepted Answer

A line with a y-intercept of -1 and a slope of 2.

Answer

A line with a y-intercept of 1 and a slope of 2.

Answer

A line with a y-intercept of 1 and a slope of -2.

Answer

A line with a y-intercept of -1 and a slope of -2.

Question 38

The perimeter of a rectangle is 30 meters. The length is 2 meters more than twice the width. What is the width of the rectangle?

Accepted Answer

4 meters

Answer

6 meters

Answer

7 meters

Answer

5 meters

Question 39

Which of the following is NOT a linear equation?

Accepted Answer

x² + 2x - 1 = 0

Answer

x - 3y = 6

Answer

2y + 4 = 10

Answer

3x - 5 = 7

Question 40

Solve for y:  3y - 8 = 14

Accepted Answer

7

Answer

11

Answer

9

Answer

5

Question 41

Solve for z:  2(z + 3) = 18

Accepted Answer

6

Answer

4

Answer

10

Answer

8

Question 42

Solve for x:  x - 5 = 3x + 7

Accepted Answer

-3

Answer

3

Answer

-1

Answer

1

Question 43

Solve for y:  2y + 3 = y - 6

Accepted Answer

-9

Answer

-3

Answer

3

Answer

9

Question 44

Solve for x:  3x + 2 = 2x - 5

Accepted Answer

7

Answer

11

Answer

5

Answer

9

Question 45

Solve for y:  2(y - 3) = 3(y + 2)

Accepted Answer

-1

Answer

1

Answer

-3

Question 46

The sum of two numbers is 50. If one number is 15, what is the other number?

Accepted Answer

35

Answer

25

Answer

45

Question 47

A rectangular garden has a length of 10 feet and a width of x feet. If the perimeter is 30 feet, what is the value of x?

Accepted Answer

5

Answer

7

Answer

3

Answer

9

Question 48

A store sells apples for $0.50 each and oranges for $0.75 each. If a customer buys x apples and y oranges and spends a total of $12, which equation represents the situation?

Accepted Answer

0.50x + 0.75y = 12

Answer

x + y = 12

Answer

0.50y + 0.75x = 12

Answer

0.50x - 0.75y = 12