Pair of Linear Equations in Two Variables — Class 10 MCQs with Answers
Class 10 CBSE Mathematics · Chapter 3
108 practice questions · 31 Easy · 39 Medium · 38 Hard · Updated
Jump to the 6 solved questions
Practise the most important Class 10 CBSE Mathematics questions from Chapter 3, "Pair of Linear Equations in Two Variables". You get 11 timed quizzes made from 108 NCERT-based MCQs, with answers and explanations. The questions are split into 31 Easy, 39 Medium and 38 Hard. Warm up on the basics, then move on to the exam-level questions that top scorers in CBSE Board exams and the JEE & NEET foundation years get right.
To score well in "Pair of Linear Equations in Two Variables", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This helps you stay accurate when time is short, just as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.
Use this chapter for focused revision. Start with the Easy set to check your basics on Pair of Linear Equations in Two Variables, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 10 Mathematics mastery score. Try the 6 sample questions below: tap an option to see the answer and a worked explanation. Sign in free to start practising.
Pair of Linear Equations in Two Variables — important questions & MCQs with answers (Class 10 Mathematics)
6 solved questions from this chapter's difficulty levels, each with its answer and explanation. Tap an option to check yourself.
0 of 6 answered
- Q1 of 6Easy
The pair x + y = 5, 2x + 2y = 10 has:
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Answer: Infinitely many solutions
Explanation: Testing a₁/a₂ = b₁/b₂ = c₁/c₂ here gives 1/2 = 1/2 = 5/10, all equal, so the two equations describe the same line, giving infinitely many solutions rather than just one.
- Q2 of 6Easy
The general form of a linear equation in two variables x and y (a, b, c real numbers, a and b not both zero) is:
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Answer: ax + by + c = 0
Explanation: A linear equation in two variables is degree-1 in each variable: ax + by + c = 0, with a and b not both zero — unlike ax² + by + c = 0, which is quadratic, not linear.
- Q3 of 6Medium
Solve: 2x + 3y = 11 and 2x − 4y = −24. Then (x, y) is:
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Answer: (−2, 5)
Explanation: Elimination: subtracting 2x−4y=−24 from 2x+3y=11 cancels x, giving 7y=35 so y=5; then 2x=11−15=−4, x=−2. Sign errors while subtracting negatives are the common trap.
- Q4 of 6Medium
Assertion (A): The lines x – 3y + 2 = 0 and 2x + y – 5 = 0 intersect at exactly one point. Reason (R): If a₁/a₂ = b₁/b₂, the lines represented by the pair intersect at a point.
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Answer: A is true but R is false
Explanation: A is true: a₁/a₂ = 1/2 and b₁/b₂ = –3, which are not equal, so the lines intersect at one point. R is false: lines intersect when a₁/a₂ ≠ b₁/b₂.
- Q5 of 6Hard
Two trains start from stations A and B and travel toward each other at speeds of 50 km/h and 60 km/h respectively. The faster train covers 120 km more than the slower one before they meet. Distance between A and B is:
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Answer: 1320 km
Explanation: Both trains run for the same time t; the 10 km/h speed gap explains the extra 120 km, so 10t=120 gives t=12 h. Distance = (50+60)×12 = 1320 km. Using one train's speed alone is the common error.
- Q6 of 6Hard
Assertion (A): The solution of the pair 3x + 2y = 12 and 5x – 2y = 4 is x = 2, y = 3. Reason (R): If the lines of a pair of linear equations coincide, the pair has infinitely many solutions.
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Answer: Both A and R are true but R is not the correct explanation of A
Explanation: A is true: adding the equations gives 8x = 16, so x = 2 and then y = 3; both equations check. R is also true, but these lines are not coincident, so R does not explain A.
Pair of Linear Equations in Two Variables notes: key concepts (Class 10 Mathematics)
Two linear equations in two variables can meet once, never, or everywhere, and the ratios of their coefficients tell you which before you solve anything. This chapter covers the graphical meaning of consistency and the substitution, elimination and cross-multiplication methods.
- Pair of linear equations
- Two equations of the form ax + by + c = 0 considered together; a solution is a pair (x, y) satisfying both at once.
- Graphical solution
- Each equation is a straight line, and the point where the lines cross is the solution of the pair.
- Consistent pair
- A pair having at least one solution — the lines either intersect at one point or coincide completely.
- Inconsistent pair
- A pair with no solution at all, whose lines are parallel and never meet.
- Unique solution condition
- When a₁/a₂ ≠ b₁/b₂ the lines have different slopes, intersect once, and the pair has exactly one solution.
- Infinitely many solutions
- When a₁/a₂ = b₁/b₂ = c₁/c₂ the two equations describe the same line, so every point on it is a solution.
- No solution condition
- When a₁/a₂ = b₁/b₂ ≠ c₁/c₂ the lines are parallel and distinct, so no pair (x, y) satisfies both.
- Substitution method
- The first of the three algebraic methods: make one variable the subject in one equation and substitute it into the other, reducing the pair to a single equation.
- Elimination method
- Multiply the equations so one variable has matching coefficients, then add or subtract to eliminate it.
- Cross-multiplication method
- A direct formula giving x and y from the six coefficients, useful when the numbers make substitution messy.
- Equations reducible to linear form
- Equations in 1/x and 1/y become linear after substituting u = 1/x and v = 1/y, then are solved as usual.
- Word problems
- Real situations — ages, speeds, digits of a number, fractions — translated into two equations by naming the unknowns carefully.
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Pair of Linear Equations in Two Variables — FAQs
What are the key concepts in Class 10 Mathematics Pair of Linear Equations in Two Variables?+
Two linear equations in two variables can meet once, never, or everywhere, and the ratios of their coefficients tell you which before you solve anything. This chapter covers the graphical meaning of consistency and the substitution, elimination and cross-multiplication methods. Key ideas include Pair of linear equations, Graphical solution, Consistent pair, Inconsistent pair, Unique solution condition, Infinitely many solutions.
What does Class 10 Mathematics Chapter 3 (Pair of Linear Equations in Two Variables) cover on XamBaaz?+
It has 108 NCERT-based MCQs on "Pair of Linear Equations in Two Variables": 31 Easy, 39 Medium and 38 Hard. Together they make 11 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE Board exams and the JEE & NEET foundation years.
Are these "Pair of Linear Equations in Two Variables" questions free to practise?+
Yes. Sign in with Google to practise "Pair of Linear Equations in Two Variables" free. Full unlimited access is ₹999/year. One year from the day you pay. You stay in Class 10 till 31 March; on 1 April your account moves up to Class 11 and the rest of your year carries over. No chapter is charged separately.
How should I revise "Pair of Linear Equations in Two Variables" for the exam?+
Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 11 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.
Are these "Pair of Linear Equations in Two Variables" MCQs available with answers?+
Yes. 6 sample questions are on this page with answers: tap an option, or "Show answer", to see the correct option and a step-by-step explanation. Sign in free with Google to start practising, with instant scoring.
Is there negative marking in the "Pair of Linear Equations in Two Variables" quizzes?+
Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.
What are the important questions from Pair of Linear Equations in Two Variables (Class 10 Mathematics)?+
The questions that matter most test Pair of linear equations, Graphical solution, Consistent pair, Inconsistent pair, Unique solution condition, Infinitely many solutions. This page shows 6 solved important MCQs with answers and explanations. Sign in to practise all 108 questions on the chapter as timed quizzes.
Is there an online quiz for Pair of Linear Equations in Two Variables?+
Yes — Class 10 Mathematics Pair of Linear Equations in Two Variables has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.
Are there question answers and extra questions for Pair of Linear Equations in Two Variables (Class 10 Mathematics)?+
Yes. This page has 6 solved questions on Pair of Linear Equations in Two Variables, each with the correct answer and a short explanation. Sign in to practise all 108 questions on the chapter as timed quizzes.
Are there assertion–reason and case study questions for Pair of Linear Equations in Two Variables (Class 10 Mathematics)?+
Yes. The Pair of Linear Equations in Two Variables question bank has 6 assertion–reason questions and 12 case-based (case study) questions in the CBSE board format, alongside the regular MCQs. Each comes with the answer and a worked explanation. Sign in to practise them in timed quizzes.