Master Systems of Equations: A Comprehensive Guide for 8th Graders

Question 1

What is the x-intercept of the line represented by the equation 3x - 2y = 6?

Accepted Answer

2

Answer

-2

Answer

3

Answer

6

Question 2

Identify the correct system of linear equations:

Accepted Answer

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

Answer

2x + 3y = 6

Answer

x^2 + y^2 = 10

Answer

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

Question 3

Which point is a solution to the system x + y = 5, x - y = 1?

Accepted Answer

(3, 2)

Answer

(2, 3)

Answer

(1, 4)

Answer

(4, 1)

Question 4

Find the value of x in the solution to 3x + 2y = 12, y = x - 2:

Accepted Answer

4

Answer

2

Answer

6

Answer

8

Question 5

To solve 2x + 3y = 7, 4x + 6y = 14, you can use:

Accepted Answer

Both graphing and substitution

Answer

Graphing

Answer

Substitution

Answer

Neither graphing nor substitution

Question 6

Find the equation of the line that passes through the points (2, 5) and (4, 1).

Accepted Answer

y = -2x + 9

Answer

y = -x + 3

Answer

y = 2x - 1

Answer

y = x + 5

Question 7

Which of the following is NOT a system of equations?

Accepted Answer

y = x^2 + 2

Answer

2x + 3y = 6

Answer

x - y = 5 and x + y = 7

Answer

y = 2x + 3

Question 8

Which of the following represents a system of linear equations?

Accepted Answer

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

Answer

y = x^2 - 1

Answer

y = |x| + 2

Answer

x^2 + y^2 = 9

Question 9

Find the y-intercept of the line represented by the equation y = -2x + 5.

Accepted Answer

5

Answer

-2

Answer

2

Answer

-5

Question 10

Which of the following is a system of two linear equations in two variables?

Accepted Answer

x + y = 5 and x - y = 2

Answer

x + y = 5

Answer

x - y = 2

Answer

x^2 + y^2 = 1

Question 11

What is the slope of the line represented by the equation 3x - 2y = 6?

Accepted Answer

3/2

Answer

2

Answer

-2

Answer

-3/2

Question 12

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

Accepted Answer

x + y = 5 and x - y = 2

Answer

x + y = 5

Answer

x^2 + y^2 = 25

Answer

y = mx + b

Question 13

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

Accepted Answer

-2

Answer

2

Answer

3

Answer

-3

Question 14

What is the x-intercept of the line represented by the equation 3x - 2y = 6?

Accepted Answer

3

Answer

0

Answer

2

Answer

6

Question 15

Which equation represents a line parallel to the x-axis?

Accepted Answer

y = 2

Answer

y = x + 1

Answer

y = -x + 2

Answer

y = 2x - 3

Question 16

Which of the following graphical representations accurately depicts a system of equations?

Accepted Answer

Two intersecting lines on a coordinate plane

Answer

A single point on a coordinate plane

Answer

Parallel lines on a coordinate plane

Answer

A circle on a coordinate plane

Question 17

Which method for solving systems of equations involves expressing one variable in terms of the other and substituting it into the second equation?

Accepted Answer

Substitution

Answer

Graphing

Answer

Elimination

Answer

Linear combination

Question 18

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

Accepted Answer

3

Answer

2

Answer

4

Answer

5

Question 19

Which of the following steps should be excluded when solving a system of equations by graphing?

Accepted Answer

Solve the equations algebraically

Answer

Plot the equations on the coordinate plane

Answer

Find the point of intersection

Answer

Verify the solution in both equations

Question 20

Which step is NOT involved in solving a system of equations by graphing?

Accepted Answer

Solve for x and y using algebra.

Answer

Plot the equations on a coordinate plane.

Answer

Identify the point of intersection.

Answer

Substitute the x-coordinate into an equation to find y.

Question 21

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 22

Which system of equations is represented by the following graph?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 23

What is the value of y when x = 3 in the equation y = 2x - 1?

Accepted Answer

5

Answer

4

Answer

6

Answer

7

Question 24

When graphing a system of linear equations, what do the points of intersection represent?

Accepted Answer

The solution(s) to the system

Answer

The slopes of the lines

Answer

The y-intercepts of the lines

Answer

The x-intercepts of the lines

Question 25

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

Accepted Answer

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

Answer

x + y = 5, x^2 - y = 3

Answer

x^3 - y^2 = 1, 2x + 3y = 4

Answer

sin(x) + cos(y) = 1, x - y = 2

Question 26

When solving a system of equations by elimination, what is the first step?

Accepted Answer

Multiply one or both equations by a constant to make the coefficients of one variable the same

Answer

Subtract one equation from the other

Answer

Substitute one variable into the other equation

Answer

Graph the system of equations

Question 27

Which property of equality states that if equals are added to equals, the results are equal?

Accepted Answer

Addition property of equality

Answer

Subtraction property of equality

Answer

Multiplication property of equality

Answer

Division property of equality

Question 28

When solving a system of equations by substitution, what is the first step?

Accepted Answer

Solve one equation for a variable and substitute it into the other equation

Answer

Multiply one or both equations by a constant to make the coefficients of one variable the same

Answer

Subtract one equation from the other

Answer

Graph the system of equations

Question 29

Which of the following is a system of linear equations?

Accepted Answer

x - y = 2, x + y = 5

Answer

x + y = 5

Answer

x = 2y - 1

Answer

y = 2x^2 + 1

Question 30

Solve the following system of equations graphically: 2x + y = 5, x - y = 1

Accepted Answer

(1, 3)

Answer

(2, 1)

Answer

(-2, 5)

Answer

(-1, 3)

Question 31

Use substitution to solve the following system of equations: x + 2y = 4, 3x - y = 5

Accepted Answer

x = 2, y = 1

Answer

x = 1, y = 2

Answer

x = -2, y = 3

Answer

x = 3, y = -2

Question 32

Solve the following system of equations: x - 3y = 5, 2x + y = 1

Accepted Answer

x = 2, y = 1

Answer

x = 1, y = 2

Answer

x = -2, y = 3

Answer

x = 3, y = -2

Question 33

Which of the following is a system of nonlinear equations?

Accepted Answer

x^2 + y^2 = 25

Answer

x + y = 5

Answer

x - y = 2, x + y = 5

Answer

y = 2x + 1

Question 34

Identify the dependent variable in the equation y = 2x + 1:

Accepted Answer

y

Answer

x

Answer

2

Answer

1

Question 35

Which method is NOT used to solve systems of equations?

Accepted Answer

Trial and error

Answer

Graphing

Answer

Substitution

Answer

Elimination

Question 36

When graphing a system of equations, what does the point of intersection represent?

Accepted Answer

Solution to the system

Answer

Slope of the system

Answer

Independent variables

Answer

Dependent variables

Question 37

Find the y-intercept of the line y = -3x + 2:

Accepted Answer

2

Answer

-3

Answer

-2

Answer

3

Question 38

The system of equations y = x and y = -x + 2 has:

Accepted Answer

Infinitely many solutions

Answer

One solution

Answer

Two solutions

Answer

No solution

Question 39

Graph the system of equations: y = 2x + 1 and y = -x + 3. Determine the coordinates of the point of intersection.

Accepted Answer

The lines intersect at (1, 3).

Answer

The lines are parallel and do not intersect.

Answer

The lines are perpendicular and intersect at (0, 0).

Question 40

Which system of equations has no solution?

Accepted Answer

x + y = 5, x + y = 7

Answer

2x + 3y = 6, 4x + 6y = 12

Answer

x - y = 3, x + y = 5

Answer

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

Question 41

Which system of equations has infinitely many solutions?

Accepted Answer

x + y = 0, 2x + 2y = 0

Answer

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

Answer

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

Answer

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

Question 42

Determine the slope of the line represented by the equation y = -2x + 3.

Accepted Answer

-2

Answer

2

Answer

3

Question 43

Write the equation of the line that passes through the point (2, 5) with a slope of 1.

Accepted Answer

y = x + 3

Answer

y = x - 3

Answer

y = -x + 7

Answer

y = 2x + 1

Question 44

Which of the following represents a system of equations?

Accepted Answer

(2 equations connected by 'and')

Answer

A set of inequalities

Answer

A single equation

Answer

(2 equations connected by 'or')

Question 45

Which system of equations has no solution?

Accepted Answer

(x + y = 5) and (x + y = 7)

Answer

(2x + 3y = 11) and (-x + y = -1)

Answer

(x + y = 5) and (x - y = 1)

Question 46

Which system of equations has infinitely many solutions?

Accepted Answer

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

Answer

(2x + 3y = 11) and (x - y = 1)

Answer

(x + y = 5) and (x - y = 1)

Answer

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

Question 47

What is the y-intercept of the line represented by the equation: y = -2x + 4?

Accepted Answer

4

Answer

-4

Answer

2

Answer

-2

Question 48

Which system of equations models a real-world scenario?

Accepted Answer

(Cost of apples + Cost of oranges = Total cost) and (Number of apples + Number of oranges = Total number of fruits)

Answer

(x + y = 5) and (x - y = 1)

Question 49

Which of the following pairs of equations represents a system of equations?

Accepted Answer

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

Answer

x = 2 and y = 3

Answer

2x - 3y = 6

Answer

x + y = 5

Question 50

Solve for x and y using the substitution method:  x + y = 5 and x - y = 1

Accepted Answer

x = 3, y = 2

Answer

x = 4, y = 1

Answer

x = 1, y = 4

Answer

x = 2, y = 3

Question 51

A farmer has 12 animals, some cows and some pigs. Each cow has 4 legs and each pig has 2 legs. If there are a total of 36 legs, how many cows are there?

Accepted Answer

6

Answer

4

Answer

10

Answer

8

Question 52

Which graph shows the solution to the system of inequalities: y > x and y < 2x?

Accepted Answer

[Image of a shaded region above the line y = x and below the line y = 2x]

Answer

[Image of a shaded region above the line y = x and y = 2x]

Answer

[Image of a shaded region above the line y = 2x and below the line y = x]

Question 53

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

Accepted Answer

2

Answer

1

Answer

4

Answer

3

Question 54

Which of these systems of equations has no solution?

Accepted Answer

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

Answer

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

Answer

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

Question 55

Find the solution to the system of equations using graphing: 2x + 3y = 6 and x - y = 1

Accepted Answer

(2, 1)

Answer

(0, 3)

Answer

(3, 0)

Answer

(1, 2)

Question 56

Solve for x and y in the system of equations: x² + y² = 25 and x - y = 3

Accepted Answer

(4, 1) and (1, 4)

Answer

(6, -1) and (-1, 6)

Answer

(5, 0) and (0, 5)

Answer

(3, 2) and (2, 3)

Question 57

Which of these steps is part of the substitution method for solving systems of equations?

Accepted Answer

Solve one equation for one variable, then substitute that expression into the other equation.

Answer

Graph both equations and find the point of intersection

Answer

Add or subtract the equations to eliminate one variable

Question 58

The sum of two numbers is 10 and their difference is 2. What are the two numbers?

Accepted Answer

6 and 4

Answer

7 and 3

Answer

8 and 2

Answer

5 and 5