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Class 10 Pair of Linear Equations Practice Questions
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CLASS 10 PAIR OF LINEAR EQUATIONS PRACTICE QUESTIONS
SECTION A — MCQs
The graphical representation of a pair of linear equations has infinitely many solutions when the lines are:
A. intersecting
B. parallel
C. coincident
D. perpendicularFor the pair of equations
2x + 3y = 11
4x + 6y = 22
the system has:
A. no solution
B. exactly one solution
C. infinitely many solutions
D. two solutionsThe pair of equations x − 2y = 4 and 3x − 6y = 12 represents:
A. intersecting lines
B. parallel lines
C. coincident lines
D. perpendicular linesIf a₁/a₂ ≠ b₁/b₂, then the pair of linear equations has:
A. no solution
B. infinitely many solutions
C. exactly one solution
D. no real solutionWhich method is most suitable for solving
7x − 2y = 5
14x − 4y = 10
A. substitution
B. elimination
C. cross-multiplication
D. graphical
SECTION B — 1-MARK QUESTIONS
Write the general form of a pair of linear equations in two variables.
How many solutions does a pair of coincident straight lines have?
Write the condition for a pair of linear equations to have no solution.
Represent the equation 3x + 2y = 6 graphically.
State whether the pair of equations
x + y = 5
x − y = 1
has a unique solution or not.
SECTION C — 2-MARK QUESTIONS
Solve the pair of equations using substitution method:
x + y = 7
x − y = 1Find the solution of the pair of equations using elimination method:
2x + 3y = 13
4x + 3y = 21Determine whether the pair of equations
3x − y = 5
6x − 2y = 10
has no solution, unique solution, or infinitely many solutions.Solve graphically:
x + y = 4
x − y = 2Find the value of k for which the pair of equations
kx + y = 3
2x + ky = 7
has infinitely many solutions.
SECTION D – 3 MARK QUESTIONS
Solve the following pair of linear equations by cross-multiplication method:
3x − 2y = 5
2x + y = 4Find the solution of the pair of equations:
4x − y = 9
2x + 3y = 13Determine the values of a for which the pair of equations
ax + 2y = 6
4x + ay = 12
has no solution.Solve graphically and find the coordinates of the point of intersection:
2x + y = 6
x − y = 1Solve the pair of equations:
7x + 2y = 18
3x − 2y = 2
SECTION E – 4 MARK QUESTIONS
Solve the pair of equations using elimination method and verify the result:
5x − 3y = 11
3x + 2y = 4Find the solution of the pair of equations using substitution method:
x − y = 2
2x + y = 7Solve the pair of equations by cross-multiplication method:
4x + 5y = 23
6x − 5y = 7Determine the nature of the solutions of the pair of equations:
2x + 3y = 11
4x + 6y = 22
SECTION F – WORD PROBLEMS
The sum of two numbers is 27 and their difference is 3. Find the numbers.
A student scored a total of 50 marks by getting 8 marks for each correct answer and losing 2 marks for each wrong answer. If he answered 10 questions, find how many were correct and wrong.
The cost of 3 pens and 2 notebooks is ₹46, while the cost of 5 pens and 4 notebooks is ₹82. Find the cost of one pen and one notebook.
Two numbers differ by 26 and their sum is 100. Find the numbers.
The sum of the digits of a two-digit number is 9. The number obtained by reversing the digits exceeds the original number by 27. Find the number.
Class 10 Pair of Linear Equations Practice Questions – Complete CBSE Chapter Guide
Class 10 Pair of Linear Equations Practice Questions are essential for mastering one of the most important algebra chapters in the CBSE Class 10 Mathematics syllabus. This chapter introduces students to solving two linear equations involving two variables using different methods and interpreting their solutions graphically and algebraically. Regular practice with Class 10 Pair of Linear Equations Practice Questions builds strong problem-solving skills and improves exam confidence.
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According to the latest CBSE blueprint, this chapter carries around 4–6 marks in the Class 10 Board Examination, making it one of the highest-weightage chapters in algebra. Questions are frequently asked in MCQ format, short-answer questions, long-answer problems, and real-life word problems. Therefore, practising only basic questions is not enough; students must solve conceptual and tricky Class 10 Pair of Linear Equations Practice Questions to score 95+.
Why Class 10 Pair of Linear Equations Practice Questions Are Very Important
Many students find this chapter challenging because it involves multiple solution methods and interpretation of results. Class 10 Pair of Linear Equations Practice Questions help students:
Understand the concept of simultaneous linear equations
Learn when a system has one solution, no solution, or infinitely many solutions
Choose the most suitable method for solving a given pair of equations
Apply algebraic concepts to real-life situations
Improve accuracy and logical reasoning
This chapter also prepares students for advanced algebra topics in higher classes.
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Topics Covered Through Class 10 Pair of Linear Equations Practice Questions
All Class 10 Pair of Linear Equations Practice Questions on this page strictly follow the latest CBSE syllabus and include questions from the following topics:
General form of a pair of linear equations in two variables
Graphical method of solving linear equations
Algebraic methods of solving equations:
Substitution method
Elimination method
Cross-multiplication method
Conditions for:
Unique solution
No solution
Infinitely many solutions
Consistency and inconsistency of equations
Real-life and word problems based on linear equations
No deleted or out-of-syllabus topics are included, ensuring focused board-exam preparation.
Exam Pattern and Trends for Pair of Linear Equations
In recent CBSE board papers, Class 10 Pair of Linear Equations Practice Questions have appeared in various forms:
MCQs testing conditions of consistency
2-mark questions on identifying the nature of solutions
3-mark questions using algebraic methods
4-mark questions involving step-wise solutions
Application-based word problems involving numbers, money, ages, and situations
Because of this variety, students must practise questions of different difficulty levels rather than relying on memorised steps.
How These Class 10 Pair of Linear Equations Practice Questions Help You Score 95+
Scoring high in this chapter depends on conceptual clarity, not speed alone. The Class 10 Pair of Linear Equations Practice Questions provided on this page are designed to:
Improve understanding of solution conditions
Strengthen algebraic manipulation skills
Help students select the correct solving method quickly
Reduce calculation and sign errors
Prepare students for unfamiliar or twisted word problems
With regular practice, students can confidently attempt any board-level question from this chapter.
Common Mistakes Students Make in This Chapter
Students often lose marks in this chapter due to:
Choosing the wrong method of solution
Incorrect elimination of variables
Poor graph plotting and interpretation
Confusion between consistent and inconsistent systems
Incomplete steps in long-answer questions
Practising structured Class 10 Pair of Linear Equations Practice Questions helps eliminate these mistakes gradually.
How to Use This Page Effectively
To make the best use of this page:
Begin with MCQs to revise key concepts
Practise short-answer questions to improve accuracy
Focus on 3-mark and 4-mark questions for board readiness
Spend extra time on word problems
Revise graphical interpretation carefully
Following this approach will make Class 10 Pair of Linear Equations Practice Questions one of your strongest scoring areas.
Who Should Use These Class 10 Pair of Linear Equations Practice Questions?
This page is useful for:
CBSE Class 10 students
Students targeting 95–99 marks
Teachers looking for exam-oriented practice material
Students revising for pre-boards and final exams
The questions are carefully designed to test fundamental understanding and deep reasoning, exactly as required in the board exam.
Final Words
The chapter Pair of Linear Equations in Two Variables is a high-weightage and high-scoring chapter when practised correctly. Solving advanced and conceptual Class 10 Pair of Linear Equations Practice Questions ensures that students do not panic during exams and can confidently solve even the toughest problems.
This page is designed to serve as a complete practice solution for mastering this chapter and achieving top scores in CBSE Class 10 Mathematics.
Daily Update: Colorful Notes, Flashcards, Tests, Worksheets, etc are shared .
Daily Update: Quizzes, Flashcards, Tests, Worksheets etc are shared .
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CBSE Class 10 Complete Exam Preparation Materials
✅ Oswaal Class 10 SST — Topper's Choice
✅ Together With SST — Best for Practice
✅ Oswaal Science Class 10 — Chapter Wise
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✅ Oswaal Class 10 SST — Topper's Choice
✅ Together With SST — Best for Practice
✅ Oswaal Science Class 10 — Chapter Wise
✅ RD Sharma Maths — Most Popular