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 (A)</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. (A)</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. (B)</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. (D)</p> Signup and view all the answers

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

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

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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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