# Chapter 2 – Linear Equations in One Variable

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

You might have experienced a situation in life where you have to choose between two things. For example, there is a supermarket that offers eight eggs for Rs. 120 and 10 eggs (8 Poultry + 2 Non-Poultry) for Rs. 200. Which deal should you go for?

This is the time when linear equations might be helpful for you.

Linear Equations in one variable are one of the simplest equations that can be better written as:

Integer(a) variable(x) + integer(b) = 0.

Where, a and b – two integers.

x – A variable

And the most crucial part is that there is only one unique solution.

Examples of Linear Equations in one variable

5y + 16 = 18

Now, let’s understand what the essential features of Linear Equations in one variable are –

1. As the name suggests, It has only one variable. In the above example, we can see that y is the variable.
2. The linear equation will have only one unique solution. In the above example, let’s try to solve the linear equation.

5y + 16 = 18

5y = 18-16

5y = 2

Y = 2/5

#### Solving Equations having the variable on both sides

It is the next step of a linear equation in one variable. Here, variables are present on both sides. But solving this one is also very simple. Let us help you with the same.

The trick here is to bring the variables on one side and constants on one side. Then you will apply the simple BODMAS rule. Let’s simplify it with an example.

8y + 14 = 6y +16

8y – 6 y = 16 – 14

2y = 2

y = 1

Above given is one of the simplest examples with addition and variables on both sides. Similarly, we can do more operations with subtraction, multiplication, and division.

#### Some More Applications

All the applications like – addition, subtraction, multiplication, and division – are possible with linear equations with one variable and linear equations with variables on both sides.

Let’s have a look –

5y*6 + 3x = 6y + 5x + 10

30y + 3x = 6y + 5x + 10 (As per the BODMAS, first multiplication will be done)

30y – 6y = 10 + 5x – 3x (Now, similar variables will be brought on one side)

24y = 10 + 2x (Simple mathematical operations will be performed)

24y – 2x = 10

2(12y – x) = 2(5) (Reducing the linear equation into the simplest form)

12 y – x = 5 (Final answer)

This is the linear equation with different applications.

#### Reducing Equations to Simpler Forms

Reducing linear equations in its simplest form is one of the easy exercises. Here you need to perform the same linear equation rule firstly. The variables need to be brought at one side, and then you must follow the BODMAS rule.

But you must remember that you need to apply the BODMAS rule to variables firstly. Try to understand it by the following example:

18y/3 + 6 = 2y + 10 (Here y is the variable)

6y + 6 = 2y + 10 (As per the BODMAS rule, division operation is being operated here first)

6y – 2 y = 10 – 6 (Now, you need to bring each variable on one side and then perform the operation)

4y = 4

y = 1 (This is the simplest form of the equation).

#### Equations Reducible to the Linear Form

It is a complex form of a linear equation. Sometimes, you can get some expressions which are not in the linear form. Begin by first trying to get it converted in the linear form. And then you can solve it quickly.

Let’s understand the same by a simple example –

x + 1/2x + 3 = 3/8

8(x+1) = 3(2x+3)

8x + 8 = 6x + 9

8x – 6x = 9 – 8

2x = 1

X = ½

So, there are some times you will observe that the expressions are complex. Thus, the first step is to convert these expressions in the simplest form of linear equations. And then you will be able to solve it easily.

#### Some Applications Linear Equations

Linear equations problems are the foundation of mathematics. You can use it to solve numerous mathematical problems.

Let’s understand it by an example:

The sum of two numbers is 48. The greater number exceeds, the smaller one by four times, the smaller number. Find both the numbers.

Let the smaller number be x. The greater number is 48 – x.

(48 – x) – x = 4x

48 – 2x = 4x (As per the BODMAS rule, bracket will be removed first)

48 = 4x + 2x (Then the variables will be moved to one side)

48 = 6x

48/6 = x (Let’s reduce the equation into the simplest form)

8 = x

Thus, the smaller number is 8 and the greater number is 48 – x = 40.

#### FAQs

1. What is a linear equation in one variable with example?

An equation which has only one unique solution and one variable can be termed as a linear equation in one variable.

For Example, 5x + 2 = 13. It is a linear equation with only one variable x. And it will have only one solution too.

Let’s solve it.

5x = 13-2

5x = 11

X = 11/5

2. What is a one variable equation?

One variable equation is another name of a linear equation in one variable. It is expressed as

integer variable + integer = 0

3. Which equations are linear?

A linear equation can be expressed as –

z = ax+b

4. Which is not a linear equation in one variable?

Linear equation in one variable has only one variable. When there are two variables, then it’s not a linear equation with one variable.

For example, 65 (x+y) is not a linear equation in one variable because it has two variables – x and y.

5. What is a linear equation explained with an example?

A linear equation has only one unique solution and two variables.

For example, 4x + 8 = 12

4x = 12 -8

4x = 4

x = 4/4

x = 1

6. What are linear equations in two variables?

Linear equations in two variables have two variables and infinite solutions.

For Example, 8x + 4y = 20

6x + 3y = 8

Solving this,

Adding both of the equations together

14x + 7y = 28

7(2x + y) = 7(4)

2x + y = 4

We believe in a fun way of learning. And with the MSVgo application, we aim to achieve just that. Have a look at their videos which will help you to understand the concept in a much better way. With real-life illustrations and their applications, we are sure that the topic will be crystal clear, and you will enjoy learning.

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