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

Flashcards

Unique solution of linear equations

Graphical representation is intersecting lines.

No solution of linear equations

Graphical representation is parallel lines.

Infinite solutions of linear equations

Graphical representation is identical lines.

Solving linear equations

Methods include substitution, elimination, graphical etc.

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Solving system of linear equations

Finding the values of variables that satisfy both equations.

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Solution for 2 equations

x = 1, y = 4 for system: x + y = 5 and 2x - y = 3.

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Solution for another 2 equations

x = 1, y = 2 for system: 3x - 2y = 7 and 2x + y = 4.

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Interpolation Method

Not a method to solve linear equations.

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Solution for 2 equations example

x = 0, y = 0 for system: 3x - 4y = 2 and 6x - 8y = 4.

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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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