Class 10 Maths Chapter 3, Pair of Linear Equations in Two Variables, studies simultaneous linear equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 both graphically (intersecting, parallel or coincident lines) and algebraically using the substitution and elimination methods.
What Class 10 Mathematics (Ganit — Hindi Medium) Chapter 3 Covers
3.1 & 3.2 Graphical Method of Solution of a Pair of Linear Equations compares the coefficient ratios a1/a2, b1/b2 and c1/c2: (1) a1/a2 ≠ b1/b2 gives intersecting lines and a unique solution (consistent); (2) a1/a2 = b1/b2 = c1/c2 gives coincident lines and infinitely many solutions (dependent and consistent); (3) a1/a2 = b1/b2 ≠ c1/c2 gives parallel lines and no solution (inconsistent).
3.3 Algebraic Methods: Substitution and Elimination solves pairs of linear equations and word problems (fractions, ages, two-digit numbers with reversed digits, fixed + per-km taxi/library charges, and monthly income/expenditure ratios) by substituting one variable in terms of the other or by multiplying equations to eliminate one variable.
Exercises in Chapter 3
- Exercise 3.1 (7 Questions) tests coefficient ratios for intersecting/parallel/coincident lines, consistency, and graphical solution of linear systems.
- Exercise 3.2 (3 Questions) covers the substitution method and word problems on supplementary angles, cricket bats/balls, taxi charges, fractions and ages.
- Exercise 3.3 (2 Questions) covers the elimination method and word problems on two-digit numbers, currency notes and lending library charges.
Read Class 10 Mathematics (Ganit — Hindi Medium) Chapter 3 Online
More Chapters
- Previous: Chapter 2: बहुपद (Polynomials)
- Next: Chapter 4: द्विघात समीकरण (Quadratic Equations)
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FAQ
When does a pair of linear equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 have no solution?
The pair of linear equations is inconsistent (parallel lines, no solution) when a1/a2 = b1/b2 ≠ c1/c2.
When does the pair have a unique solution or infinitely many solutions?
It has a unique solution (intersecting lines) when a1/a2 ≠ b1/b2, and infinitely many solutions (coincident lines) when a1/a2 = b1/b2 = c1/c2.