# NCERT Solutions for Class 9 Maths Chapter 4 – Linear Equations in Two Variables

NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables are the best study resource to solve all your doubts in the NCERT textbook exercises. Chapter 4 NCERT Solutions for Class 9 Maths is an extension of ‘Linear Equations in One Variable’ that you learned in your previous Classes. Thus you will get an opportunity to recall the core concepts of Linear Equations while solving the questions of this Chapter.

There are 4 exercises which include 16 questions on all the methods to find the Solutions of Linear Equation with Two Variables. NCERT Solutions will help you prepare topics like Graph of Linear Equation with Two Variables, Equations of lines parallel to the x-axis and y-axis and methods to solve Linear Equation with Two Variables. Some of these exercises will also require you to find Solutions using graphical technical techniques.

The NCERT exercise questions are both objective and subjective so you will be able to practice all the concepts of the Chapter in a comprehensive manner. Maths experts at Instasolv have prepared NCERT Solutions for Class 9 Maths Chapter 4 in a step-wise manner to include all the information you might require to solve the questions. This resource is highly recommended if you have NCERT Class 9 Maths Book in your syllabus. This will help you improve your marks in Maths and clear all your doubts at once.

## Important Points of NCERT Solutions for Class 9 Maths Chapter 4 Introduction

- Any equation which can be put in the form ax + by + c = 0; where a, b, and c are real numbers, and a and b are not both zero, is known as a Linear Equation in Two Variables.

- Examples of Linear Equations in Two Variables are the equations of the type ax + b = 0 as they can be translated into the following expression: ax + 0.y + b = 0

**Important Rules**

The Solutions of a Linear Equation remain unaffected when:

- We add or subtract the same number from both sides of the equation.
- We multiply or divide both sides of the equation by the same non-zero number.

### Solutions of a Linear Equation in Two Variables

- In this case, a Solutions would mean a pair of values, one for x and one for y which satisfy the given equation, because there are two variables in the equation.
- The Solutions is written as an ordered pair (x,y) writing the values of x and y in the given order.
- A Linear Equation in two variables can have infinitely many solutions.

### Geometric Representation of a Linear Equation in Two Variables

- An equation in two variables with degree 1 can be represented geometrically by the line whose points make up the collection of Solutions of the equation.
- Therefore, every point on this line would satisfy the given equation.
- This line of solutions is known as the graph of the Linear Equation.
- Hence, to obtain this line, it is enough to plot two points corresponding to the Solutions and join them by a line. However, it is advisable that we plot two or more points for checking the correctness of the graph immediately after drawing the line.

### Equations of Lines Parallel to the x-axis and y-axis

- On the x-axis, the y-coordinate of each point is 0 and is of the form (x,0). Hence, the equation of x-axis is given as y = 0; which can be expressed as 0.x + 1.y = 0.
- Similarly, the equation of the y-axis is given by the expression, x = 0.
- The graph of the equation x = a is a straight line parallel to the y-axis where a is a constant.
- The graph of the equation y = b is a straight line parallel to the x-axis where b is a constant.
- An equation of the type y = mx represents a line passing through the origin O.

### Highlights of NCERT Class 9 Maths Chapter 4 Linear Equation in Two Variables

- A Linear Equation in Two Variables can be expressed in the form: ax + by + c = 0, such that a, b, and c are real numbers and a and b are not both zero.
- Such an equation has infinite solutions.
- The graph of Linear Equation is always a straight line.
- x = 0 and y = 0 are equations of the y-axis and x-axis respectively.
- Every solution of the Linear Equation is a point of the graph for the same.

### Discussion of Exercises of NCERT Solutions for Class 9 Maths Chapter 4

- NCERT Class 9 Maths Chapter 4 Exercise 4.1 consists of beginner-level questions which will require you to write the equations in the form of linear expression for the given word problems.
- Exercise 4.2 has a variety of questions ranging from State True or False to finding the value of a given term in the Linear Equation.
- Exercise 4.3 helps you with a robust practice of representation of equations in the form of a linear graph. By preparing the NCERT Solutions for this exercise, you will learn to find correct answers for such questions quickly.
- Exercise 4.4 is very important for the topics that you will study higher classes. It is necessary that you prepare all the NCERT Solutions for Class 9 Maths Chapter 4.

### Benefits of NCERT Solutions for Class 9 Maths Chapter 4 provided by Instasolv

- Instasolv provides NCERT Solutions for Class 9 Maths Chapter 4 keeping in mind, the CBSE exam pattern and guidelines. Therefore, you can rest assured about the relevance of the answers.
- You will find the answers prepared by the Instasolv professionals very easy to understand.
- These NCERT Class 9 Maths Solutions are also reliable for quick last-minute revision to help you boost your confidence before sitting in the stressful exam environment.
- NCERT Solutions for Chapter 4 will help you develop strong fundamentals for competitive exams as well.
- We, at Instasolv, make sure that we leave no stone unturned in respect of quality and simplicity of the answers.
- We have covered each and every topic thoroughly along with all the questions, so you can unhesitatingly reach out to us in search of all your doubts.