Class 10 Maths Chapter 3 Most Important Questions Pair of Linear Equations CBSE
Preparing for the CBSE Class 10 Maths Board Exam 2026–27? In this post, you will find the most important questions from Chapter 3 – Pair of Linear Equations in Two Variables, along with useful video solutions and exam-oriented practice. These questions cover important concepts such as substitution method, elimination method, graphical method, consistency of a pair of linear equations, and important word problems. Watch the videos, practise each question yourself, and strengthen your preparation for the CBSE examination. Pair of Linear Equations in Two Variables A pair of linear equations in two variables consists of two linear equations involving the same two variables, usually represented by (x) and (y). In Class 10 Maths, this chapter focuses on finding the solution of such equations using graphical, substitution and elimination methods. Students also learn how to determine whether a pair of linear equations has a unique solution, no solution, or infinitely many solutions. The chapter includes important word problems and application-based questions, making it an important topic for CBSE Board Exam preparation. Class 10 Maths Chapter 3 – Pair of Linear Equations in Two Variables The chapter Pair of Linear Equations in Two Variables is important because questions can test both your conceptual understanding and your ability to solve problems step by step. You should be comfortable with: Standard Form of Pair of Linear Equations in Two Variables 3. Identify Whether a Pair Has a Unique Solution, No Solution or Infinitely Many Solutions This is one of the most important conceptual areas of the chapter. For a pair of linear equations, we can determine whether the equations have a unique solution, no solution, or infinitely many solutions by comparing their coefficients. For the equations: a₁x + b₁y + c₁ = 0a₂x + b₂y + c₂ = 0 we use the following conditions: 1. Unique solution a₁/a₂ ≠ b₁/b₂ 2. No solution a₁/a₂ = b₁/b₂ ≠ c₁/c₂ 3. Infinitely many solutions a₁/a₂ = b₁/b₂ = c₁/c₂ Students should learn these conditions carefully because they can appear directly as questions or as part of a larger problem. Most Important Concepts – Chapter 3 The following questions cover the most important concepts and question patterns from Chapter 3 – Pair of Linear Equations in Two Variables. These are selected to help students prepare for the CBSE 2026–27 examination and strengthen their understanding of both direct and application-based questions. In this section, we will solve important examples using the three methods prescribed for this chapter: Substitution Method, Elimination Method and Graphical Method. Step-by-step solutions are provided so that students can understand the method clearly and apply it to similar questions in the examination. 1. Substitution Method In the substitution method, we first express one variable in terms of the other from either of the two equations. We then substitute this value in the second equation to find the required variables. 2. Elimination Method In the elimination method, we multiply one or both equations by suitable numbers so that the coefficient of one variable becomes the same or opposite. We then add or subtract the equations to eliminate that variable. 3. Graphical Method In the graphical method, we represent both linear equations as straight lines on a graph. The point where the two lines intersect gives the solution of the pair of linear equations. These three methods are important for Class 10 Maths Chapter 3, so students should practise questions using each method and understand when and how each method is applied. 1. Solve Using the Substitution Method Students should practise questions where one equation can easily be rearranged and substituted into the other. Question:Solve the following pair of linear equations by the substitution method: x + y = 72x − y = 5 Solution Given: x + y = 7 …(1) 2x − y = 5 …(2) From equation (1): y = 7 − x Now substitute the value of y in equation (2): 2x − (7 − x) = 5 2x − 7 + x = 5 3x − 7 = 5 3x = 12 x = 4 Now substitute x = 4 in equation (1): 4 + y = 7 y = 3 Answer x = 4 and y = 3 Therefore, the solution of the pair of linear equations is (4, 3). 2. Solve a Pair of Linear Equations by Elimination Method Questions requiring students to eliminate one variable are frequently useful for practising the standard solving procedure. Example: Question 1 Solve the following pair of linear equations by the elimination method: 2x + 3y = 113x − 2y = 4 Solution Given: 2x + 3y = 11 …(1) 3x − 2y = 4 …(2) Multiply equation (1) by 2: 4x + 6y = 22 …(3) Multiply equation (2) by 3: 9x − 6y = 12 …(4) Adding equations (3) and (4): 4x + 6y + 9x − 6y = 22 + 12 13x = 34 Therefore, x = 34/13 Now substitute x = 34/13 in equation (1): 2(34/13) + 3y = 11 68/13 + 3y = 143/13 3y = 75/13 Therefore, y = 25/13 Answer x = 34/13 and y = 25/13 3. Graphical Interpretation of a Pair of Linear Equations The graphs of two linear equations help us understand the number of solutions. Understanding this visually makes the consistency concept much easier. Question:Solve the following pair of linear equations graphically: x + y = 72x − y = 5 Solution We will find some values of x and y for each equation and plot the corresponding points on the graph. Equation (1): x + y = 7 x 0 4 7 y 7 3 0 Equation (2): 2x − y = 5 x 0 3 4 y −5 1 3 Chapter 3 Pair of Linear Equations Important Word Problem Questions Word problems are an important part of this chapter. While preparing, practise questions involving: The most important skill is converting the information given in the question into two linear equations. Example The sum of two numbers is 27 and their
