Linear Equations and Inequalities in Two Variables Quiz

Test your knowledge on linear equations, inequalities, slopes, and solutions with this algebra quiz. Practice identifying lines, solving systems, and understanding shaded regions.

Practice Learn Test

Which of the following equations represents a linear equation in two variables?

y = x^2 + 3

3x - 2y = 5

2y = 4x + 1

xy = 7

What is the solution to the linear equation 2x - 3y = 6?

(3, 0)

(0, 2)

(2, 0)

(0, 3)

Which of the following represents a vertical line?

y = 2x + 3

x = 4

y = -3x - 2

y = 4x - 1

What is the y-intercept of the line given by the equation 4y = 8x - 16?

(-2, 0)

(0, -4)

(0, 4)

(2, 0)

What is the slope-intercept form of the equation 3x + 2y = 8?

y = 3/2x + 4

y = -3/2x + 4

y = -3/2x + 8

y = 3/2x - 8

Which of the following inequalities represents a shaded region above the line?

y ≤ 2x + 3

y ≥ 4x - 1

y < -x + 2

y > 3x + 2

What is the slope of the line passing through the points (2, 5) and (4, 9)?

Which of the following represents a solution to the system of linear equations: 3x - y = 5 and x + 2y = 8?

(2, -1)

(1, 2)

(3, 0)

(4, 2)

What is the solution set to the inequality 2x + 3y < 6?

(-∞, ∞)

{(x, y) | x + y < 2}

{(x, y) | x + y > 2}

{(x, y) | x + y = 2}

#10

What is the solution to the system of equations: 2x + 3y = 7 and x - 2y = 3?

(1, 2)

(2, 1)

(3, 1)

(1, 3)

#11

Which of the following systems of linear inequalities is represented by the shaded region below?

y ≥ 2x - 1 ; y < 3x + 2

y < -2x + 1 ; y ≥ x - 3

y > -x + 3 ; y ≤ 2x + 4

y ≤ 4x - 2 ; y > x + 1

#12

What is the solution to the system of inequalities: y > 2x - 1 and y ≤ -x + 4?

(-∞, ∞)

{(x, y) | x < 1, y > 1}

{(x, y) | x > 1, y > 1}

{(x, y) | x > 1, y < 1}

#13

Which of the following represents the solution set to the inequality system: x + y ≤ 4 and x - y > 1?

{(x, y) | x ≤ 2, y ≤ 2, x > 1}

{(x, y) | x > 2, y ≤ 2, x > 1}

{(x, y) | x ≤ 2, y > 2, x > 1}

{(x, y) | x ≤ 2, y ≤ 2, x ≤ 1}

#14

What is the solution to the inequality system: y < 2x + 1 and y > -x + 3?

(-∞, ∞)

{(x, y) | x > -1, y < 1}

{(x, y) | x > 1, y > 1}

{(x, y) | x < 1, y > 1}

#15

What is the slope of the line perpendicular to the line with equation y = -2x + 4?

-2

-1/2

1/2

Linear Equations and Inequalities in Two Variables Quiz

Which of the following equations represents a linear equation in two variables?

What is the solution to the linear equation 2x - 3y = 6?

Which of the following represents a vertical line?

What is the y-intercept of the line given by the equation 4y = 8x - 16?

What is the slope-intercept form of the equation 3x + 2y = 8?

Which of the following inequalities represents a shaded region above the line?

What is the slope of the line passing through the points (2, 5) and (4, 9)?

Which of the following represents a solution to the system of linear equations: 3x - y = 5 and x + 2y = 8?

What is the solution set to the inequality 2x + 3y < 6?

What is the solution to the system of equations: 2x + 3y = 7 and x - 2y = 3?

Which of the following systems of linear inequalities is represented by the shaded region below?

What is the solution to the system of inequalities: y > 2x - 1 and y ≤ -x + 4?

Which of the following represents the solution set to the inequality system: x + y ≤ 4 and x - y > 1?

What is the solution to the inequality system: y < 2x + 1 and y > -x + 3?

What is the slope of the line perpendicular to the line with equation y = -2x + 4?

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