Linear Inequalities in Two Variables Quiz
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Questions and Answers

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

  • The set of all negative integers (x, y) that satisfy the inequality
  • The set of all positive integers (x, y) that satisfy the inequality
  • The set of all points (x, y) that satisfy the inequality (correct)
  • The set of all points (x, y) that do not satisfy the inequality

    • For the inequality -3x + 4y >= 12, what region does the solution set lie in?

  • The region below the line
  • The region above the line (correct)
  • The region to the right of the line
  • The region to the left of the line

    • What happens to the solution set of an inequality 4x - 5y > 20 if both sides of the inequality are divided by a negative number?

  • The solution set remains unchanged
  • The solution set becomes the entire coordinate plane
  • The solution set becomes the empty set
  • The solution set flips across the x-axis (correct)

    • Which type of line represents the boundary for an inequality 3x - 2y <= 6?

    <p>A solid line</p> Signup and view all the answers

    In the inequality 5x - 3y > 15, what happens to the solution set if both sides of the inequality are multiplied by a negative number?

    <p>The inequality sign changes, and the solution set is reversed.</p> Signup and view all the answers

    For the inequality -2x + 7y < 21, in which region does the solution set lie?

    <p>Above the line represented by -2x + 7y = 21.</p> Signup and view all the answers

    Which type of line represents the boundary for the inequality 6x - y > 12?

    <p>Solid line with a shading above it.</p> Signup and view all the answers

    What is the solution set for the inequality 4x + 5y ≤ 20?

    <p>$4x + 5y &lt; 20$</p> Signup and view all the answers

    Study Notes

    Inequality Solution Sets

    • The solution set for the inequality 2x + 3y < 6 lies in the region where the value of the expression is less than 6.
    • The solution set for the inequality -3x + 4y >= 12 lies in the region where the value of the expression is greater than or equal to 12.

    Boundary Lines

    • The boundary for the inequality 3x - 2y <= 6 is a solid line, indicating that the points on the line are included in the solution set.
    • The boundary for the inequality 6x - y > 12 is a dashed line, indicating that the points on the line are not included in the solution set.

    Effect of Operations on Solution Sets

    • If both sides of an inequality are divided by a negative number, the direction of the inequality is reversed, and the solution set is also reversed.
    • If both sides of an inequality are multiplied by a negative number, the direction of the inequality is reversed, and the solution set is also reversed.
    • The solution set for the inequality 4x - 5y > 20 is reversed if both sides of the inequality are divided by a negative number.
    • The solution set for the inequality 5x - 3y > 15 is reversed if both sides of the inequality are multiplied by a negative number.

    Specific Inequalities

    • The solution set for the inequality 4x + 5y ≤ 20 lies in the region where the value of the expression is less than or equal to 20.
    • The solution set for the inequality -2x + 7y < 21 lies in the region where the value of the expression is less than 21.

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    Description

    Test your knowledge on linear inequalities in two variables with this quiz. Explore the solution sets, regions, and the impact of dividing both sides by a negative number in different inequality scenarios.

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