Download Free PDF of RS Aggarwal Solutions Class 10 Chapter 3 - Linear Equations in Two Variables (Ex 3I) Exercise 3.9 Available on Vedantu
FAQs on RS Aggarwal Solutions Class 10 Chapter 3 - Linear Equations in two variables (Ex 3I) Exercise 3.9
1. How do the step-by-step RS Aggarwal Solutions for Chapter 3 help in preparing for the Class 10 board exams?
Vedantu’s RS Aggarwal Solutions for Chapter 3, Linear Equations in Two Variables, are curated by subject matter experts to align with the latest CBSE 2025-26 syllabus. They help in exam preparation by:
Providing a clear, step-by-step methodology for solving every problem in Exercise 3.9.
Helping students understand how to translate complex word problems into algebraic equations.
Reinforcing the correct application of methods like Elimination and Substitution, which are crucial for scoring full marks.
Highlighting common areas where students might make mistakes, ensuring better accuracy and time management during the exam.
2. What is the standard form of a pair of linear equations in two variables as per the Class 10 syllabus?
The standard form for a pair of linear equations in two variables, x and y, is:
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
Here, a₁, b₁, c₁, a₂, b₂, and c₂ are real numbers, and it is important that a₁² + b₁² ≠ 0 and a₂² + b₂² ≠ 0. This form is essential for applying algebraic methods and determining the nature of the solution.
3. What are the conditions for a pair of linear equations to have a unique solution, no solution, or infinitely many solutions?
For a pair of linear equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, the nature of the solution depends on the ratio of their coefficients:
Unique Solution: If a₁/a₂ ≠ b₁/b₂. The lines representing the equations intersect at exactly one point.
No Solution: If a₁/a₂ = b₁/b₂ ≠ c₁/c₂. The lines are parallel and never intersect.
Infinitely Many Solutions: If a₁/a₂ = b₁/b₂ = c₁/c₂. The lines are coincident, meaning they are the same line.
4. When solving problems from RS Aggarwal Chapter 3, when is it better to use the elimination method over the substitution method?
Choosing the right method can save time and reduce errors. Here’s a simple guide:
Use the elimination method when the coefficients of one of the variables (either x or y) in both equations are the same, opposites, or can be easily made the same by multiplying one or both equations by a small integer. This method is generally faster for such cases.
Use the substitution method when one of the variables in either equation has a coefficient of 1 or -1, making it easy to express that variable in terms of the other without creating complex fractions.
5. Why is it necessary to convert word problems into a pair of linear equations before solving them?
Converting word problems into a pair of linear equations is a crucial first step because it translates a real-world scenario into a structured mathematical format. This process helps to:
Identify the unknowns and assign variables (like x and y) to them.
Establish relationships between these unknowns based on the conditions given in the problem.
Create a systematic framework that allows for the application of proven algebraic methods like substitution or elimination to find a precise and verifiable solution.
Without this step, solving complex problems with multiple conditions would be confusing and prone to errors.
6. How can you check if your solution (x, y) for a system of linear equations from Exercise 3.9 is correct?
To verify the correctness of your solution for a pair of linear equations, you must substitute the values of x and y back into both of the original equations. Your solution is correct only if it satisfies both equations simultaneously. If the values make the left-hand side (LHS) equal to the right-hand side (RHS) for both equations, the solution is verified.
7. What are some common mistakes to avoid while solving linear equations from RS Aggarwal Class 10 Chapter 3?
Students often make a few common mistakes while solving problems in this chapter. Be careful to avoid the following:
Sign Errors: Incorrectly handling negative signs during addition, subtraction, or transposition of terms is the most frequent error.
Incorrect Equation Formulation: Misinterpreting the conditions of a word problem and setting up the wrong initial equations.
Calculation Mistakes: Simple arithmetic errors when multiplying equations or substituting values.
Incomplete Solution: Finding the value of only one variable (e.g., x) and forgetting to solve for the second variable (y).
