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NCERT Solutions for Class 8 Maths Chapter 2 Linear Equations in One Variable

## NCERT Solutions for Class 8 Maths Chapter 2 Linear Equations in One Variable - Free PDF

Suppose you are looking for the simplest and easiest way of understanding Class 8 Maths Chapter 2 concepts, then you must avail of Linear Equations in One Variable Class 8 CBSE Solutions created by the expert team of Vedantu. Keeping in mind the understanding level of class 8 students, the scholars have designed the NCERT Solutions for Class 8 Maths Chapter 2 after a lot of research. The solutions also adhere to the latest CBSE guidelines; hence students can expect to get good grades in maths after going through our Class 8 Maths NCERT Solution Chapter 2. You can also download NCERT Solutions for Class 8 Science on our website.

## NCERT Solutions for Class 8 Maths Chapter 2 Linear Equations in One Variable - PDF Download

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## Chapter 2 - Linear Equations in One Variable

### 2.1 Introduction

In the introduction part of NCERT Maths Class 8 Chapter 2, you will be reminded of algebraic equations and expressions of earlier days. Those are of the format shown below:

Expresiones - 5x + y, x + y, y + y2, etc.

Equations - 5x + y = 10, x + y = -2, y + y2= 9 etc.

From these examples, you can see that equations have an equality sign (=), which is not present in expressions.Â Algebraic expression involves variables, constants, and some mathematical operations like addition or multiplication. An equation is an expression that equates two expressions.

Students would learn the history of algebraic equations and their definitions. They would also get an idea of what is coming up in the chapter in this section.

### 2.2 Solving Equations With Linear Expression on One SIde and Numbers on the Other Side

This section of Maths NCERT Solutions Class 8 Chapter 2 starts by recalling the method for solving equations like the one shown below:

Â 5x - 3 = 8

We solve this by adding 3 on both sides so we get

Â 5x - 3 + 3 = 8 + 3

5x = 11, hence x = 2.2

The above example is a linear expression where the highest power of a variable is only 1. A linear equation that involves one variable can be marked on a straight line. A linear equation can be in one or more than one variable.

You are then presented with a few examples which are based on the method of solving linear equations as described above.

### 2.3 Some Applications

In this topic, students will go through some applications of linear equations which are in the form of puzzles. There are many wordy samples solved which involve some real-life situations like calculating age, counting money, etc.

### 2.4 Solving Equations that Have Variables on Both Sides

Till now, the chapter has dealt with equations where the value on the right-hand side of the equality sign has been only numbers. In this section, we will look into problems where there are variables on both sides of the equation. An example of such an equation is:Â

2x - 5 = x +3

Solution -> 2x = x + 3 + 5

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Subtracting x from both sides we get 2x - x = x + 8 - x

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â So, x = 8

You are then given many solved examples of such equations and an exercise on it with 10 questions.

### 2.6 Reducing Equations to Simpler Forms

A complex linear equation that has fractions in it can be reduced into a simpler form by the process described below:

Take the LCM(Least common multiple) of the denominator.

Now multiply both RHS and LHS of the equation with this LCM.

By applying the above multiplication, the equation gets reduced to a form without the denominator in it.

Then you can apply the methods learned in the sections above to solve such problems.

We will explain this with an example:

x/2 - 1/5 = x/3 + 1/4 + 1

To reduce the above equation into a simpler form, let us take the LCM of the denominators, i.e. 2, 5, 3, and 4, which is 60. Now multiply each term on both sides of the equation with 60.

60* x/2 - 1/5Â * 60 = x/3 * 60 + 1/4Â * 60 + 1 * 60

30x - 12 = 20x + 15 + 60

30x - 12 = 20x + 75

Now we will move all the expressions with variables to the LHS and all the constant to the RHS, so we get:

30x - 20x = 75 + 12

10x = 87

X = 87/10 = 8.7

### We Cover All Exercises of Chapter 2 - Linear Equations in One Variable Given Below

EXERCISE 2.1 - 12 Questions with Solutions

EXERCISE 2.2 - 16 Questions with Solutions

EXERCISE 2.3 - 10 Questions with Solutions

EXERCISE 2.4 - 10 Questions with Solutions

EXERCISE 2.5 - 10 Questions with Solutions

EXERCISE 2.6 - 7 Questions with Solutions.

### Key Features of NCERT Solutions for Class 8 Maths Chapter 2

The Class 8 Maths Chapter 2 Solution provided by Vedantu is the most reliable online resource for the revision and preparation of CBSE exams. The key benefits of these solutions are:

The solutions are simple to understand and broken into steps so that students can grasp the concept perfectly.

You can also download the solutions in PDF format or print them for a group study, making exam time revisions quick and convenient.

The solutions are based entirely on the CBSE curriculum; hence you are well prepared for your exams once you go through our solutions.

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1. Give an example of an equation that is not a linear equation but can be reduced to a linear form.

Sometimes we come across equations that are not linear as per the definition of linear equations but can be reduced to a linear form and then the method of solving linear equations can be applied to them to solve them. The example below illustrates one such equation and how to solve it:

(X + 1)/(2x + 6) = 3/8

To reduce this nonlinear equation into a linear equation we multiply both sides by the denominator of LHS which is 2x + 6.

(X + 1)/(2x + 6) * (2x + 6) = 3/8 * (2x + 6)

X + 1 = 6x + 18/8 - This is a linear equation now. We can solve it by multiplying both sides with LCM of denominators which is 8

8 * (x + 1) = 8 * (6x + 18/8)

8x + 8 = 6x + 18

Now moving all variable to LHS and all constant to RHS we get:

8x - 6x = 18 - 8

2x = 10

X = 5

2. Mention some of the important features of a linear equation.

A linear equation is characterized by the following key properties:

The highest power of the variable involved in a linear equation is 1.

The linear equation can have one or two variables in it.

A linear equation has an equality sign. The expression on the left side of the equality is called LHS (left-hand side), and the expression on the right side of the equality sign is termed as RHS (right-hand side).

The two expressions, LHS and RHS, are equal for only certain values of the variables. These values of the variables are the solutions of the linear equation.

The points of a linear equation with just one variable can be marked on the number line.