RS Aggarwal Solutions Class 8 Chapter-8 Linear Equations (Ex 8A) Exercise 8.1

Q: 3. What is the most common mistake students make when solving questions from RS Aggarwal Class 8, Exercise 8A?

The most common mistake is an error in signs during transposition. When moving a term from one side of the equation to the other, students often forget to change its sign. For instance, moving a '–7' from the LHS to the RHS should make it '+7'. Forgetting this simple rule leads to an incorrect answer. The provided RS Aggarwal solutions clearly show this sign change in each step, helping students avoid this common pitfall.

RS Aggarwal Solutions Class 8 Chapter-8 Linear Equations (Ex 8A) Exercise 8.1 - Free PDF

Becoming an algebra expert will lead you to open new doors to help you build a better career. You need to be good at math solving to understand the concepts of computer science, and even in the medicine stream, this Rs Aggarwal math class 8 exercise 8a solution is going to help you. In Rs Aggarwal class 8 math ch 8 ex 8a, you will be learning to solve one of the most used mathematical equations. Which you will be using over and over again in incoming classes.

The linear equation is something which students need to put their time and effort into understanding completely. With math, Rs Aggarwal solutions class 8 exercise 8a, students get to have experience solving different types of problems, including linear equations and algebra. Not only with this article, but you will also be able to have Rs Aggarwal class 8 math chapter 8 exercise 8a solutions. But you will be learning innovative ways and shortcuts to check if your answer is correct or not?

Vedantu also provides free NCERT Solution and other study materials for students. You can also download NCERT Solutions for Class 8 Math and Class 8 Science to help you to revise the complete syllabus and score more marks in your examinations.

The advantage of solving a system of linear equations by graphing is that it is relatively easy to do and requires very little algebra, and the main disadvantage is that your answer will be approximate due to having to read the answer from a graph.

Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable. A linear equation can have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on. Some of the examples of linear equations are 2x – 5 = 0, 2x = 8, m + 1 = 0, y/2 = 3, z+ y = 2, 3y – x + z = 3. In this article, we are going to discuss the definition of linear equations, standard form for linear equations in one variable, two variables, three variables and their examples with complete explanation.

How to Solve Linear Equations?

To solve linear equations in 2 variables, there are different methods. Following are some of them:

Method of substitution
Cross multiplication method
Method of elimination

We must choose a set of 2 equations to find the values of 2 variables. Such as ax + by + c = 0 and dx + ey + f = 0, also called a system of equations with two variables, where x and y are two variables and a, b, c, d, e, f are constants, and a, b, d and e are not zero. Else, the single equation has an infinite number of solutions.

Solution of Linear Equations in Three Variables

To solve linear equations in 3 variables, we need a set of 3 equations as given below to find the values of unknowns. Matrix method is one of the popular methods to solve a system of linear equations with 3 variables.

a₁x + b₁y + c₁z + d₁ = 0

a₂x + b₂y + c₂z + d₂ = 0 and

a₃x + b₃y + c₃z + d₃ = 0

FAQs on RS Aggarwal Solutions Class 8 Chapter-8 Linear Equations (Ex 8A) Exercise 8.1

1. What is the correct step-by-step method to solve the linear equations in RS Aggarwal Class 8 Maths, Exercise 8A?

The solutions for RS Aggarwal Class 8 Maths, Exercise 8A, primarily use the transposition method. This involves moving terms from one side of the equation to the other to isolate the variable. The key steps are:

Identify the variable and the constant terms in the equation.
Move all terms containing the variable to one side (usually the Left-Hand Side or LHS) and all constant terms to the other side (Right-Hand Side or RHS).
When a term is moved to the other side, its sign is reversed (e.g., '+' becomes '–' and '×' becomes '÷').
Simplify the equation to find the value of the variable.
Finally, you can verify your answer by substituting the value back into the original equation.

2. How can I verify my answer for a problem in Chapter 8, Linear Equations, using the RS Aggarwal solutions format?

To verify your solution for any linear equation, you must check if the Left-Hand Side (LHS) of the equation equals the Right-Hand Side (RHS) after substituting the value of the variable you found. For example, if you solve an equation and find that x = 5, substitute '5' for 'x' in the original equation. If both sides of the '=' sign result in the same number, your answer is correct. This verification step is a crucial part of the problem-solving methodology as per the CBSE pattern.

3. What is the most common mistake students make when solving questions from RS Aggarwal Class 8, Exercise 8A?

The most common mistake is an error in signs during transposition. When moving a term from one side of the equation to the other, students often forget to change its sign. For instance, moving a '–7' from the LHS to the RHS should make it '+7'. Forgetting this simple rule leads to an incorrect answer. The provided RS Aggarwal solutions clearly show this sign change in each step, helping students avoid this common pitfall.

4. How do the problems in RS Aggarwal's Exercise 8A compare to those in the NCERT textbook for Class 8 Linear Equations?

The problems in RS Aggarwal's Exercise 8A are designed to build upon the concepts introduced in the NCERT textbook. While NCERT provides foundational problems, RS Aggarwal offers a greater number and variety of practice questions. This helps reinforce the core solving methods, like transposition and verification, ensuring students gain confidence and speed. Using RS Aggarwal solutions after trying the NCERT exercises is an effective strategy for mastering the chapter.

5. Why does the 'transposition' method actually work for solving linear equations in Chapter 8?

Transposition is essentially a shortcut for a fundamental mathematical rule: an equation remains balanced if you perform the exact same operation on both sides. For example, when you 'transpose' a '+3' to the other side and make it '–3', what you are actually doing is subtracting '3' from both the LHS and the RHS. The shortcut just makes the process faster. Understanding this principle is key to grasping why the step-by-step methods shown in the solutions are mathematically correct.

6. How do the RS Aggarwal solutions for Chapter 8 help in setting up and solving word problems?

While Exercise 8A focuses on basic equations, the principles taught are foundational for word problems in later exercises. The solutions demonstrate the critical first step: translating the text of a problem into a mathematical statement. They guide you on:

Identifying the unknown quantity and assigning a variable (like 'x') to it.
Forming a linear equation based on the relationships described in the problem.
Applying the systematic solving method to find the value of the variable.
Interpreting the result in the context of the original word problem.

7. What is the best way to use Vedantu's RS Aggarwal Solutions for Class 8 Maths, Chapter 8, to improve my marks?

For maximum benefit, do not simply copy the answers. The best approach is to first attempt to solve the exercise problems on your own. Use the solutions as a tool for verification or as a guide when you are genuinely stuck on a particular step. By comparing your method with the detailed, step-by-step solutions, you can identify your mistakes, understand the correct procedure, and strengthen your grasp of the concepts for the 2025-26 academic year exams.