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.
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
