Understanding the key concepts of Class 10 Maths Chapter 3 – Pair of Linear Equations in Two Variables is crucial for exam success. To make your revision easier, we have created chapterwise mcq questions with Answers for class 10 Maths based on the latest syllabus and exam pattern. It is a part of MCQ Questions for CBSE Class 10 Maths Series.
These multiple-choice questions will help you assess your knowledge, improve accuracy, and boost confidence for your exams. Whether you are preparing for school tests, online tests or competitive exams, these Pair of Linear Equations in Two Variables MCQs will strengthen your conceptual clarity.
| Chapter | Pair of Linear Equations in Two Variables |
| Book | Maths Textbook for Class 10 |
| Type of Questions | MCQ Questions |
| Nature of Questions | Competency Based Questions |
| Board | CBSE |
| Class | 10 |
| Subject | Maths |
| Useful for | Class 10 Studying Students |
| Answers provided | Yes |
| Difficulty level | Mentioned |
| Important Link | Class 10 Maths Chapterwise MCQ Questions |
MCQ Questions on Pair of Linear Equations in Two Variables Class 10 Maths (PDF Download)
MCQs
Q1. If a pair of linear equations has infinitely many solutions, then the lines representing them must be:
(a) Intersecting
(b) Parallel
(c) Coincident
(d) None of these
Show Answer
Answer: (c)
Explanation: Infinitely many solutions occur when the lines are coincident (exactly the same).
Q2. The equations 2x + 3y = 6 and 4x + 6y = 12 have:
(a) No solution
(b) Unique solution
(c) Infinitely many solutions
(d) Exactly two solutions
Show Answer
Answer: (c)
Explanation: These are multiples of each other and represent the same line ⇒ infinitely many solutions.
Q3. Which of the following systems is inconsistent?
(a) x + y = 2 and 2x + 2y = 4
(b) 3x + 2y = 5 and 6x + 4y = 10
(c) x + y = 3 and 2x + 2y = 10
(d) None
Show Answer
Answer: (c)
Explanation: If ratios of a₁/a₂ = b₁/b₂ ≠ c₁/c₂, the system is inconsistent ⇒ no solution.
Q4. If the graphs of two linear equations are parallel lines, what can you conclude?
(a) They have one solution
(b) They are dependent
(c) They have no solution
(d) They intersect
Show Answer
Answer: (c)
Explanation: Parallel lines never meet ⇒ no solution ⇒ inconsistent system.
Q5. Which of the following is true if two equations have a unique solution?
(a) Lines are parallel
(b) Lines coincide
(c) Lines intersect at one point
(d) Lines intersect at many points
Show Answer
Answer: (c)
Explanation: A unique solution exists if the lines intersect at exactly one point.
Q6. If a pair of equations is dependent and consistent, what is the geometrical representation?
(a) Intersecting lines
(b) Parallel lines
(c) Coincident lines
(d) None
Show Answer
Answer: (c)
Explanation: Dependent and consistent ⇒ same line ⇒ infinite solutions.
Q7. What is the solution of the equations x + y = 5 and x – y = 1?
(a) x = 3, y = 2
(b) x = 2, y = 3
(c) x = 1, y = 4
(d) x = 4, y = 1
Show Answer
Answer: (a)
Explanation: Adding and subtracting gives x = 3, y = 2.
Q8. A pair of linear equations has a unique solution when:
(a) Lines are parallel
(b) a₁/a₂ ≠ b₁/b₂
(c) a₁/a₂ = b₁/b₂ = c₁/c₂
(d) None
Show Answer
Answer: (b)
Explanation: Unique solution ⇔ a₁/a₂ ≠ b₁/b₂
Q9. If two equations are inconsistent, the graph shows:
(a) Lines intersecting
(b) Lines overlapping
(c) Lines parallel
(d) None
Show Answer
Answer: (c)
Explanation: Inconsistent ⇔ no solution ⇔ parallel lines
Q10. If the solution of a system is x = 1, y = 2, which of the following could be one of the equations?
(a) x + y = 4
(b) x + y = 3
(c) x + 2y = 5
(d) 2x + y = 6
Show Answer
Answer: (c)
Explanation: x + 2y = 1 + 4 = 5 ⇒ valid equation.
Q11. If a pair of linear equations has no solution, what is the determinant of the coefficient matrix?
(a) Non-zero
(b) Zero
(c) Undefined
(d) Imaginary
Show Answer
Answer: (b)
Explanation: If the lines are parallel (no solution), then the determinant of the coefficient matrix is zero.
Q12. Which of the following systems of equations has infinitely many solutions?
(a) 2x + 3y = 6, 4x + 6y = 10
(b) 2x + 3y = 6, 4x + 6y = 12
(c) x – y = 1, 2x – 2y = 5
(d) x + y = 1, x – y = 2
Show Answer
Answer: (b)
Explanation: Second equation is multiple of the first ⇒ same line ⇒ infinitely many solutions.
Q13. If the pair of equations 3x + 2y = 5 and 6x + 4y = k have infinitely many solutions, the value of k is:
(a) 5
(b) 10
(c) 0
(d) 15
Show Answer
Answer: (b)
Explanation: Check ratio: a₁/a₂ = b₁/b₂ = c₁/c₂ ⇒ 3/6 = 2/4 = 5/k ⇒ k = 10
Q14. The pair of equations x + y = 5 and x – y = 3 is solved. What is the product of the solutions?
(a) 8
(b) 10
(c) 15
(d) None of these
Show Answer
Answer: (a)
Explanation: x = 4, y = 1 ⇒ product = 4 × 1 = 4
Q15. If x = 2, y = 3 satisfies a pair of linear equations, what must be true?
(a) 2x + 3y = 12
(b) x + y = 6
(c) x – y = –1
(d) x = y
Show Answer
Answer: (c)
Explanation: 2 – 3 = –1 ⇒ matches (x – y = –1)
Q16. A pair of equations is given by ax + by = c and dx + ey = f. If ae – bd = 0, then:
(a) System is always consistent
(b) System is always inconsistent
(c) Cannot say without values of c and f
(d) Solution is unique
Show Answer
Answer: (c)
Explanation: ae – bd = 0 means determinant = 0 ⇒ might be dependent or inconsistent. Need RHS to determine.
Q17. If the equations x + ky = 3 and 2x + 6y = 6 represent coincident lines, what is the value of k?
(a) 2
(b) 3
(c) 1
(d) None of these
Show Answer
Answer: (a)
Explanation: Matching ratios: 1/2 = k/6 ⇒ k = 3
Q18. If a system of equations is such that the ratio of coefficients is equal but constants differ, then:
(a) Lines are coincident
(b) Lines are intersecting
(c) Lines are parallel
(d) Lines are undefined
Show Answer
Answer: (c)
Explanation: Equal ratio of coefficients and unequal constants ⇒ parallel lines ⇒ no solution.
Q19. If the equations are inconsistent, what is the geometrical representation?
(a) Intersecting lines
(b) Coincident lines
(c) Parallel lines
(d) Same point
Show Answer
Answer: (c)
Explanation: Inconsistent systems ⇒ parallel lines.
Q20. In a word problem, if one quantity is expressed as a linear function of another, it leads to:
(a) Only quadratic equations
(b) Exponential equations
(c) Pair of linear equations
(d) Polynomial equations
Show Answer
Answer: (c)
Explanation: Such situations form a pair of linear equations in two variables.
We hope the given mcq questions with Answers for Pair of Linear Equations in Two Variables Class 10 helps you in your learning.
Also check
- Arithmetic Progressions – Class 10 Maths Chapter 5 MCQ Questions with Answers (Updated)
- Quadratic Equations – Class 10 Maths Chapter 4 MCQ Questions with Answers (Updated)
- Pair of Linear Equations in Two Variables – Class 10 Maths Chapter 3 MCQ Questions with Answers (Updated)
- Polynomials – Class 10 Maths Chapter 2 MCQ Questions with Answers (Updated)
- Real Numbers – Class 10 Maths Chapter 1 MCQ Questions with Answers (Updated)
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Topics from which mcq questions may be asked
- Graphical method
- Substitution, elimination methods
- Word problems
Linear equations build the foundation for algebraic thinking and real-world problem solving.
Frequently Asked Questions (FAQs) on Pair of Linear Equations in Two Variables MCQ Questions
Q1: Why should I practice Class 10 Maths Chapter 3 MCQs?
A1: Practicing MCQs helps in quick revision, improves problem-solving speed, and enhances conceptual understanding of important topics in Class 6 Maths.
Q2: Are these Class 10 Maths MCQs based on the latest syllabus?
A2: Yes, all the MCQs are designed as per the latest CBSE syllabus and exam pattern to help students prepare effectively.
Q3: Where can I find more MCQs for Class 10 Maths?
A3: You can find more chapter-wise MCQs on our website. These are designed to cover important concepts and prepare you for exams.
Q4: Are the answers provided for all MCQs?
A4: Yes, each MCQ is accompanied by the correct answer and explanations to help students understand and learn better.
Q5: How can I improve my performance in Class 10 Maths MCQs?
A5: To improve your performance, practice regularly, revise key concepts, and take mock tests to assess your knowledge.
Q6: Do these MCQs help in school exams?
A6: Yes, these MCQs are aligned with school exam patterns and help in scoring well by strengthening conceptual clarity.
Q7: Can I download these MCQs for offline practice?
A7: Yes, you can download or print these MCQs for convenient offline practice.
Q8: Q6: Are there any resources available online for students to practice mcq questions on class 10 maths chapter 3 “Pair of Linear Equations in Two Variables“ for CBSE exams?
A6: Yes, several educational websites offer mcq questions for CBSE students preparing for maths examinations. We also offer a collection of mcq questions for all classes and subject on our website. Visit our website to access these questions and enhance your learning experience. for more mcq, you can also visit Physics Gurukul Website.
