Revision Notes: Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables

A fast, one-glance recap of Class 10 Maths Chapter 3 (Pair of Linear Equations in Two Variables) — for the full worked explanations, see the Solutions. These Class 10 Mathematics Chapter 3 notes are ideal for quick revision just before exams.

Last Updated: July 21, 2026

Why This Chapter Matters

Pair of Linear Equations in Two Variables is one of the standard chapters in the CBSE/NCERT Class 10 Maths syllabus and questions from it appear regularly in board exams, in formats ranging from 1-mark objective questions to longer 3-5 mark descriptive or numerical questions. Because the concepts here often build on earlier chapters (and feed into later ones), a solid grip on this chapter also makes the rest of the Maths syllabus easier to follow.

Revision Notes: Pair of Linear Equations in Two Variables

• Linear equation in two variables: ax + by + c = 0 (a, b not both zero)
• Pair of linear equations: a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0
• Graphical meaning: two lines can be intersecting, parallel, or coincident
• Ratio test: a₁/a₂ ≠ b₁/b₂ → intersecting, consistent, unique solution
• a₁/a₂ = b₁/b₂ ≠ c₁/c₂ → parallel, inconsistent, no solution
• a₁/a₂ = b₁/b₂ = c₁/c₂ → coincident, consistent, infinitely many solutions
• Algebraic methods: substitution (express one variable in terms of the other and substitute) and elimination (make one variable’s coefficient equal in both equations, then add/subtract)
• Word problems: define both variables clearly first, form two equations from the given conditions, solve, then sanity-check the answer fits the context (ages, speeds, costs must be positive)
• Reciprocal substitution trick: for speed/time problems with terms like 1/(x−y) and 1/(x+y), substitute u = 1/(x−y), v = 1/(x+y) to reduce to a simple linear pair
• Know by heart: the ratio-test table above is a near-guaranteed 1-2 mark question every year

See also: Extra Questions (HOTS) | Formulas Handbook

How to Use These Notes

These revision notes are meant for quick recall in the last few days before an exam or unit test — they are not a substitute for first reading the full chapter and working through examples in the NCERT textbook. A good routine is: read the chapter once, solve the in-text and end-of-chapter questions using the linked Solutions, then come back to this page a day or two before the exam to refresh the key definitions and formulas without re-reading the whole chapter.

Written by Satish

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