NCERT Solutions for Class 10 Maths Chapter 3: Pair of Linear Equations in Two Variables
For students looking for step-by-step NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables, Myclass24 offers the most comprehensive and student-friendly solutions available online. This chapter is one of the highest-weightage topics in the CBSE Class 10 Maths paper, covering multiple methods of solving linear equations and their real-life applications.
Chapter 3 is unique in the sense that it combines algebraic methods with graphical representation, making it both visual and analytical. At Myclass24, we have solved each problem using all relevant methods — graphical, substitution, elimination, and cross-multiplication — so that students understand which approach is fastest for a given problem type. The chapter also includes important real-life word problems that test a student's ability to frame equations from given conditions, which is a skill tested heavily in board examinations. With the right practice using Myclass24's solutions, students not only crack Chapter 3 questions but also improve their overall problem-solving approach in mathematics.
Download PDF – NCERT Solutions for Class 10 Maths Chapter 3 Linear Equations
Myclass24 provides a free, downloadable PDF of NCERT Solutions for Class 10 Maths Chapter 3 covering Exercise 3.1 through Exercise 3.7. The PDF is optimised for mobile devices and can be easily read on any screen size, making it ideal for students who prefer digital study materials over printed books.
Chapter 3 – Key Concepts, Solution Methods & Exercise Overview
Chapter 3 starts with the graphical method of solving a pair of linear equations. Two lines on a graph can either intersect at one point (unique solution), be parallel (no solution), or coincide (infinitely many solutions). These three scenarios correspond to consistent, inconsistent, and dependent systems, respectively. The algebraic methods taught in this chapter — substitution, elimination, and cross-multiplication — are powerful tools. The cross-multiplication method is particularly efficient when coefficients are complex. The chapter also introduces equations reducible to linear form, where substitution transforms non-linear equations into simple linear ones — a skill that appears in higher-level competitive exams as well.
| Exercise | Topics Covered | No. of Questions |
| Exercise 3.1 | Graphical Method | 3 |
| Exercise 3.2 | Substitution Method | 7 |
| Exercise 3.3 | Elimination Method | 3 |
| Exercise 3.4 | Cross-Multiplication Method | 2 |
| Exercise 3.5 | Equations Reducible to Linear Form | 4 |
| Exercise 3.6 | Word Problems – Applications | 2 |
| Exercise 3.7 | Additional Problems (Optional) | 8 |
| Type of System | Graphical Appearance | Number of Solutions | Algebraic Condition |
| Consistent (Unique) | Lines intersect | Exactly 1 | a₁/a₂ ≠ b₁/b₂ |
| Inconsistent | Lines are parallel | No solution | a₁/a₂ = b₁/b₂ ≠ c₁/c₂ |
| Dependent (Consistent) | Lines coincide | Infinitely many | a₁/a₂ = b₁/b₂ = c₁/c₂ |
A key fact students must remember: the cross-multiplication method gives the solution as x/(b₁c₂ - b₂c₁) = y/(c₁a₂ - c₂a₁) = 1/(a₁b₂ - a₂b₁). This formula looks complicated but is very systematic once practised. Word problems in Exercise 3.6 and Exercise 3.7 are gold for board exams — they involve scenarios like age problems, number problems, boat-and-stream, work problems, and geometry-based linear equation problems. CBSE frequently picks 4–5 mark word problems directly from these exercises.
| Method | Best Used When | Speed | CBSE Preference |
| Substitution | One variable is easily expressed | Medium | Common |
| Elimination | Coefficients are equal or easily matched | Fast | Most Common |
| Cross-Multiplication | Direct formula, coefficients complex | Fastest | High |
| Graphical | Need to show nature of system visually | Slow | MCQ/VSA |