Master the Concepts of Pair of Linear Equations in Two Variables with this NCERT...
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Questions and Answers

Which of the following statements is true about a pair of linear equations in two variables?

  • All of the above (correct)
  • They can have no solution
  • They can have infinitely many solutions
  • They can have one solution

    • What is the graphical representation of a pair of linear equations in two variables that have a unique solution?

  • None of the above
  • Intersecting lines (correct)
  • Parallel lines
  • Coincident lines

    • What is the condition for a pair of linear equations in two variables to have no solution?

  • The lines intersect at more than one point
  • None of the above
  • The lines are parallel (correct)
  • The lines are coincident

    • Quina és la solució del sistema d'equacions següent? x + y = 5 2x - y = 3

    <p>x = 1, y = 4</p> Signup and view all the answers

    Quina és la condició perquè un sistema d'equacions lineals en dues variables tingui una infinida solució?

    <p>Les dues equacions són paral·leles</p> Signup and view all the answers

    Quina és la solució del sistema d'equacions següent? 3x - 4y = 2 6x - 8y = 4

    <p>x = 0, y = 0</p> Signup and view all the answers

    Which of the following is NOT a method to solve a pair of linear equations in two variables?

    <p>Interpolation method</p> Signup and view all the answers

    What is the solution of the pair of linear equations 3x - 2y = 7 and 2x + y = 4?

    <p>x = 1, y = 2</p> Signup and view all the answers

    What is the condition for a pair of linear equations in two variables to have infinitely many solutions?

    <p>The equations have the same slope and the same y-intercept</p> Signup and view all the answers

    Study Notes

    Pair of Linear Equations in Two Variables

    • A pair of linear equations in two variables can have a unique solution, no solution, or infinitely many solutions.

    Graphical Representation

    • The graphical representation of a pair of linear equations in two variables with a unique solution is two intersecting lines.

    Condition for No Solution

    • The condition for a pair of linear equations in two variables to have no solution is that the two lines are parallel and do not intersect.

    Solving Systems of Equations

    • The solution to the system of equations x + y = 5 and 2x - y = 3 is x = 2 and y = 3.

    Condition for Infinitely Many Solutions

    • The condition for a pair of linear equations in two variables to have infinitely many solutions is that the two lines coincide.

    Solving Another System of Equations

    • The solution to the system of equations 3x - 4y = 2 and 6x - 8y = 4 is no solution, as the lines are parallel and do not intersect.

    Methods to Solve a Pair of Linear Equations

    • The methods to solve a pair of linear equations in two variables are substitution, elimination, and graphical method.
    • Guessing is NOT a method to solve a pair of linear equations in two variables.

    Solving Another System of Equations

    • The solution to the system of equations 3x - 2y = 7 and 2x + y = 4 is x = 3 and y = 1.

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    Description

    Test your understanding of Pair of Linear Equations in Two Variables with this quiz based on Chapter 3 of NCERT Math Class 10. Explore the properties of linear equations and learn about the graphical representation of a pair of linear equations with unique solutions. Identify the conditions for no solution and improve your knowledge of this fundamental concept in mathematics.

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