Linear Inequations and Graphical Representation
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Questions and Answers

What is the highest power of the variable in a linear inequality?

  • 2
  • 0
  • 1 (correct)
  • 3
  • How many variables are involved in a linear inequality in two variables?

  • Two (correct)
  • Three
  • Four
  • One
  • Which method is used to solve a system of linear inequalities algebraically?

  • Both A and B (correct)
  • Substitution Method
  • Elimination Method
  • Graphical Method
  • What happens to the sign of an inequality when both sides are multiplied or divided by a negative number?

    <p>The sign is reversed</p> Signup and view all the answers

    Which property states that if a > b and b > c, then a > c?

    <p>Transitive Property</p> Signup and view all the answers

    How are linear inequalities represented graphically?

    <p>Both A and B</p> Signup and view all the answers

    Why is it important to multiply or divide both sides of an inequality by a positive number?

    <p>To avoid changing the sign of the inequality</p> Signup and view all the answers

    Study Notes

    Linear Inequations

    Definition

    • A linear inequation is an inequality in which the highest power of the variable(s) is 1.
    • It can be represented as ax + by >, <, ≥, ≤ cx + dy, where a, b, c, and d are constants.

    Types of Linear Inequations

    • Simple Linear Inequation: Involves only one variable.
      • Example: 2x - 3 > 5
    • Linear Inequation in Two Variables: Involves two variables.
      • Example: 2x + 3y > 7

    Graphical Representation

    • Linear inequations can be represented on a number line or a graph.
    • The solution region is the section of the number line or graph that satisfies the inequation.

    Methods of Solving Linear Inequations

    • Substitution Method
    • Graphical Method
    • Algebraic Method

    Properties of Linear Inequations

    • Transitive Property: If a > b and b > c, then a > c.
    • Addition Property: If a > b, then a + c > b + c.
    • Multiplication Property: If a > b and c > 0, then ac > bc.

    Solving Systems of Linear Inequations

    • Graphical Method: Shade the common region of the two inequations.
    • Algebraic Method: Solve the system of inequations by substitution or elimination method.

    Important Points

    • Always multiply or divide both sides of the inequation by a positive number to avoid changing the sign of the inequation.
    • Always reverse the sign of the inequation when multiplying or dividing both sides by a negative number.

    Linear Inequations

    Definition

    • Linear inequations have the highest power of the variable(s) as 1.
    • Can be represented as ax + by >, <, ≥, or ≤.
    • Example: 2x + 3y > 7 is a linear inequation in two variables.

    Graphical Representation

    • Linear inequations can be represented on a number line or graph.
    • The solution region is the section of the number line or graph that satisfies the inequation.

    Methods of Solving Linear Inequations

    • Substitution Method: Substitute the value of one variable into the other equation.
    • Graphical Method: Represent the inequations on a graph and find the solution region.
    • Algebraic Method: Solve the inequations using algebraic operations.

    Properties of Linear Inequations

    • Transitive Property: If a > b and b > c, then a > c.
    • Addition Property: If a > b, then a + c > b + c.
    • Multiplication Property: If a > b and c > 0, then ac > bc.

    Solving Systems of Linear Inequations

    • Graphical Method: Shade the common region of the two inequations.
    • Algebraic Method: Solve the system of inequations by substitution or elimination method.

    Important Points

    • Always multiply or divide both sides of the inequation by a positive number to avoid changing the sign.
    • Reverse the sign of the inequation when multiplying or dividing both sides by a negative number.

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    Quiz Team

    Description

    Learn about linear inequations, their definition, types, and graphical representation. Understand simple linear inequations and linear inequations in two variables.

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