Class 10 Mathematics — Chapter 3: Pair of Linear Equations in Two Variables
59 practice questions · 22 Easy · 20 Medium · 17 Hard
Practise Class 10 Mathematics Chapter 3, "Pair of Linear Equations in Two Variables", with 59 NCERT-aligned multiple-choice questions. The set is split into 22 Easy, 20 Medium and 17 Hard questions, so you can warm up on the fundamentals and then push into the exam-level problems that separate top scorers in CBSE Board exams and the JEE & NEET foundation years.
"Pair of Linear Equations in Two Variables" is one of the chapters where problem-solving speed, formula recall and step-by-step reasoning really pays off. Each MCQ on this chapter is timed and uses exam-grade marking (+2 correct, −1 wrong, 0 skipped), training the same accuracy-under-pressure that real papers demand. Every question carries a short explanation, so a wrong answer becomes a quick lesson rather than a dead end — the fastest way to close gaps before a test.
Use this chapter as targeted revision: attempt the Easy set first to confirm your basics on Pair of Linear Equations in Two Variables, then move to Medium and Hard to test application and problem-solving. Your accuracy, streaks and XP save automatically, and the chapter feeds into your overall Class 10 Mathematics mastery score. A few sample questions are shown below; sign in free to practise all 59.
Key concepts: Pair of Linear Equations in Two Variables (Class 10 Mathematics)
Two linear equations in x and y can be solved together graphically or algebraically. The ratios of their coefficients tell you in advance how many solutions exist.
- Graphical meaning
- Each equation is a straight line. The solution is the point(s) where the lines meet.
- Consistent vs inconsistent
- Intersecting lines → one solution (consistent); coincident lines → infinitely many (consistent, dependent); parallel lines → no solution (inconsistent).
- Substitution method
- Express one variable from one equation and substitute into the other.
- Elimination method
- Make the coefficient of one variable equal in both equations, then add or subtract to eliminate it.
Key formulas — Pair of Linear Equations in Two Variables
💡 Exam tips for Pair of Linear Equations in Two Variables
- Write both equations as ax + by + c = 0 before comparing ratios.
- Parallel lines (no solution) and coincident lines (infinite solutions) differ only in the c-ratio.
Sample questions
The pair x + y = 5, 2x + 2y = 10 has:
Both equations are equivalent (lines coincide).
Solve: x + y = 7, x − y = 1.
Adding: 2x=8 ⇒ x=4, y=3.
Sum of two numbers is 20, difference is 4. Larger number = ?
x+y=20, x−y=4 ⇒ x=12, y=8.
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 x and y can be solved together graphically or algebraically. The ratios of their coefficients tell you in advance how many solutions exist. Key ideas include Graphical meaning, Consistent vs inconsistent, Substitution method, Elimination method.
What does Class 10 Mathematics Chapter 3 (Pair of Linear Equations in Two Variables) cover on XamBaaz?+
It covers 59 NCERT-aligned MCQs on "Pair of Linear Equations in Two Variables" — 22 Easy, 20 Medium and 17 Hard — each with a timed quiz and an instant explanation, suitable 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 (limited-time launch price), with no per-chapter charges.
How should I revise "Pair of Linear Equations in Two Variables" for the exam?+
Start with the Easy quiz to confirm your fundamentals, then attempt Medium and Hard for application-level practice. Review each explanation, retry the questions you miss, and track your accuracy on this chapter until it is consistently high.
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