Home » MCQ on Class 10 Mathematics Chapter 3 | Pair of Linear Equations in Two Variables

MCQ on Class 10 Mathematics Chapter 3 | Pair of Linear Equations in Two Variables

By Abdur Rohman / July 4, 2024

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Chapter 3 of class 10 Mathematics as per the NCERT syllabus is Pair of Linear Equations in Two Variables which deals with the Graphical Method of Solution, Algebraic Methods including Substitution Method, etc.

Here, we have discussed 30 Multiple Choice Questions based on these topics of the chapter. These questions will help you to learn more about the chapter and test your knowledge.

For each question below, there are four options out of which only one option is correct. After selecting your answer, click on the submit button to see the score and review your answers.

MCQ on Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables

1. What is the general form of a pair of linear equations in two variables?

A. \( a_1x + b_1y + c_1 = 0 \) B. \( a_2x + b_2y = c_2 \) C. \( a_1x = b_1y + c_1 \) D. \( x = a_1 + b_1y \)

2. If the pair of linear equations \(a_1x + b_1y = c_1\) and \(a_2x + b_2y = c_2\) has a unique solution, the lines representing them are:

A. Parallel B. Coincident C. Intersecting D. None of these

3. Which of the following methods is used to solve a pair of linear equations graphically?

A. Substitution B. Plotting the equations on a graph C. Elimination D. Cross-multiplication

4. If the lines \(a_1x + b_1y = c_1\) and \(a_2x + b_2y = c_2\) are parallel, what type of solution does the pair have?

A. No solution B. Unique solution C. Infinitely many solutions D. None of these

5. The graphical representation of the pair of equations \(2x + 3y = 5\) and \(4x + 6y = 10\) will be:

A. Intersecting lines B. Parallel lines C. Concurrent lines D. Coincident lines

6. The method of solving linear equations by expressing one variable in terms of the other is called:

A. Elimination B. Substitution C. Graphical method D. Cross-multiplication

7. In the substitution method, if the resulting equation after substitution is an identity (true for all values of the variable), the system of equations has:

A. Infinitely many solutions B. No solution C. Unique solution D. None of these

8. For the pair of equations \(3x + 4y = 7\) and \(6x + 8y = 14\), the lines are:

A. Intersecting B. Parallel C. Coincident D. None of these

9. Which method involves multiplying the equations by suitable non-zero constants to make the coefficients of one variable numerically equal?

A. Substitution B. Elimination C. Cross-multiplication D. Graphical method

10. When solving by elimination, if the resulting equation is a contradiction (false statement), the system of equations has:

A. No solution B. Unique solution C. Infinitely many solutions D. None of these

11. The pair of equations \(x + y = 5\) and \(2x + 2y = 10\) are:

A. Intersecting lines B. Parallel lines C. Concurrent lines D. Coincident lines

12. The graphical representation of the equations \(y = 3x + 2\) and \(y = 3x – 4\) are:

A. Coincident lines B. Parallel lines C. Intersecting lines D. None of these

13. In the pair of linear equations, if the ratio of coefficients of \(x\) and \(y\) are equal and the ratio of constant terms is not equal, the system has:

A. Unique solution B. Infinitely many solutions C. No solution D. None of these

14. If the system of equations has no solution, the lines representing the equations are:

A. Parallel B. Coincident C. Intersecting D. None of these

15. What is the graphical representation of the pair of equations \(2x – y = 1\) and \(4x – 2y = 2\)?

A. Intersecting lines B. Parallel lines C. Concurrent lines D. Coincident lines

16. Which of the following is an example of a pair of inconsistent equations?

A. \(x + y = 2\) and \(x – y = 2\) B. \(2x + 3y = 5\) and \(4x + 6y = 10\) C. \(x + 2y = 3\) and \(2x + 4y = 6\) D. \(x – y = 3\) and \(2x + y = 5\)

17. If \(a_1/a_2 = b_1/b_2 = c_1/c_2\), the pair of linear equations \(a_1x + b_1y + c_1 = 0\) and \(a_2x + b_2y + c_2 = 0\) is:

A. Inconsistent B. Consistent C. Dependent D. None of these

18. For the equations \(x + y = 3\) and \(2x + 2y = 6\), the solutions are:

A. Infinitely many solutions B. No solution C. Unique solution D. None of these

19. What is the condition for a pair of linear equations to have a unique solution?

A. \(a_1/a_2 = b_1/b_2\) B. \(a_1/a_2 \neq b_1/b_2\) C. \(a_1/a_2 = b_1/b_2 = c_1/c_2\) D. \(a_1/a_2 = c_1/c_2\)

20. If the pair of equations \(a_1x + b_1y = c_1\) and \(a_2x + b_2y = c_2\) are consistent and dependent, the lines are:

A. Intersecting B. Coincident C. Parallel D. None of these

21. In the elimination method, if the coefficients of one variable are not equal, we:

A. Multiply the equations by suitable constants to make them equal B. Subtract one equation from the other C. Divide the equations by the coefficients D. None of these

22. Which of the following represents a system of equations with no solution?

A. \(x + y = 2\) and \(x – y = 2\) B. \(2x + 3y = 5\) and \(4x + 6y = 10\) C. \(x + 2y = 3\) and \(2x + 4y = 7\) D. \(x – y = 3\) and \(2x + y = 5\)

23. The cross-multiplication method is used to solve which type of equations?

A. Quadratic equations B. Cubic equations C. Polynomial equations D. Linear equations

24. The graphical representation of \(x – y = 2\) and \(2x – 2y = 4\) will be:

A. Intersecting lines B. Parallel lines C. Coincident lines D. None of these

25. If the pair of linear equations are consistent, then the lines:

A. Intersect at exactly one point or are coincident B. Are parallel C. Are perpendicular D. None of these

26. If the ratio of the coefficients of \(x\) and \(y\) of two equations are equal, but the ratio of the constants is different, the lines will be:

A. Intersecting B. Coincident C. Parallel D. None of these

27. The elimination method involves which of the following steps?

A. Adding the equations B. Subtracting the equations C. Multiplying the equations D. All of the above

28. What is the result when a pair of linear equations has infinitely many solutions?

A. The lines are intersecting B. The lines are coincident C. The lines are parallel D. None of these

29. If \(a_1/a_2 \neq b_1/b_2\), the pair of equations \(a_1x + b_1y = c_1\) and \(a_2x + b_2y = c_2\) have:

A. No solution B. Infinitely many solutions C. A unique solution D. None of these

30. Which method would you use to solve the pair of equations \(4x + 2y = 10\) and \(2x + y = 5\) easily?

A. Substitution method B. Graphical method C. Cross-multiplication method D. Elimination method

Review Your Answers Above.

The Bottom Line

I hope these 30 MCQs on Pair of Linear Equations in Two Variables of Class 10 Maths Chapter 3 have helped you in your studies and preparation.

If you have any queries, or comments or find any mistake in the above questions, feel free to contact me in the comment section below.

I would love to hear from you.

Abdur Rohman

Abdur Rohman is an Electrical Engineer from Charaideo, Assam, who wears multiple hats as a part-time teacher, blogger, entrepreneur, and digital marketer. Passionate about education, he founded The Assam School blog to provide free, comprehensive textbook solutions, MCQs (Multiple Choice Questions), and other academic content for students from Class V to XII.

MCQ on Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables

1. What is the general form of a pair of linear equations in two variables?

2. If the pair of linear equations \(a_1x + b_1y = c_1\) and \(a_2x + b_2y = c_2\) has a unique solution, the lines representing them are:

3. Which of the following methods is used to solve a pair of linear equations graphically?

4. If the lines \(a_1x + b_1y = c_1\) and \(a_2x + b_2y = c_2\) are parallel, what type of solution does the pair have?

5. The graphical representation of the pair of equations \(2x + 3y = 5\) and \(4x + 6y = 10\) will be:

6. The method of solving linear equations by expressing one variable in terms of the other is called:

7. In the substitution method, if the resulting equation after substitution is an identity (true for all values of the variable), the system of equations has:

8. For the pair of equations \(3x + 4y = 7\) and \(6x + 8y = 14\), the lines are:

9. Which method involves multiplying the equations by suitable non-zero constants to make the coefficients of one variable numerically equal?

10. When solving by elimination, if the resulting equation is a contradiction (false statement), the system of equations has:

11. The pair of equations \(x + y = 5\) and \(2x + 2y = 10\) are:

12. The graphical representation of the equations \(y = 3x + 2\) and \(y = 3x – 4\) are:

13. In the pair of linear equations, if the ratio of coefficients of \(x\) and \(y\) are equal and the ratio of constant terms is not equal, the system has:

14. If the system of equations has no solution, the lines representing the equations are:

15. What is the graphical representation of the pair of equations \(2x – y = 1\) and \(4x – 2y = 2\)?

16. Which of the following is an example of a pair of inconsistent equations?

17. If \(a_1/a_2 = b_1/b_2 = c_1/c_2\), the pair of linear equations \(a_1x + b_1y + c_1 = 0\) and \(a_2x + b_2y + c_2 = 0\) is:

18. For the equations \(x + y = 3\) and \(2x + 2y = 6\), the solutions are:

19. What is the condition for a pair of linear equations to have a unique solution?

20. If the pair of equations \(a_1x + b_1y = c_1\) and \(a_2x + b_2y = c_2\) are consistent and dependent, the lines are:

21. In the elimination method, if the coefficients of one variable are not equal, we:

22. Which of the following represents a system of equations with no solution?

23. The cross-multiplication method is used to solve which type of equations?

24. The graphical representation of \(x – y = 2\) and \(2x – 2y = 4\) will be:

25. If the pair of linear equations are consistent, then the lines:

26. If the ratio of the coefficients of \(x\) and \(y\) of two equations are equal, but the ratio of the constants is different, the lines will be:

27. The elimination method involves which of the following steps?

28. What is the result when a pair of linear equations has infinitely many solutions?

29. If \(a_1/a_2 \neq b_1/b_2\), the pair of equations \(a_1x + b_1y = c_1\) and \(a_2x + b_2y = c_2\) have:

30. Which method would you use to solve the pair of equations \(4x + 2y = 10\) and \(2x + y = 5\) easily?

The Bottom Line

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