# 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-

In our previous classes, we have studied linear equations in one variable. In this chapter, we will study linear equations in two variables of the type ax+by+c=0 where a, b and c are the real numbers, and a and b both are not zero. In this chapter, there is a total of 4 exercises with 16 questions.  The NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables are designed by our subject experts to help students in their preparation of CBSE final examination of class 9 Maths exam as well as in the various competitive exams like Indian National Olympiad (INO), National Talent Search Examination or NTSE etc. These NCERT solutions are the detailed explanation of each and every problem of NCERT Class 9 Maths textbook.

NCERT Class 9 Maths Chapter 4 Linear Equations in Two Variables falls under the Algebra unit. This unit holds 20 marks in the CBSE final exam. We already studied linear equations in two variable in 8th class, in this class we are going to learn about linear equation in two variables.

$\dpi{100} x + 1 = 0, 5x + 2 = 0$

and

$\dpi{100} 2y + 3 = 0$ are the examples of linear equations in one variable and $\dpi{100} x + y = 5$ and $\dpi{100} x - 3y = 3$

are examples of linear equations in two variable. In this chapter we will deal with problems related to proving the linear equation has an infinite number of solutions, draw a linear equation on the graph and justification of particular point on the line. In this chapter we will also deal with problems like what is the equations of lines parallel to x- and y-axis, for example, the graph of x = a is a straight line parallel to y-axis and graph of y = a is a straight line parallel to x-axis.

Example:

Write each of the following equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:

$\\(i) 2x + 3y = 4.37\\\\(ii) x -4 = \sqrt{3}y\\\\(iii) 4 = 5x - 3y\\\\(iv) 2x = y$

Solution-

(i)

$\dpi{100} 2x + 3y = 4.37$ can be written as $\dpi{100} 2x + 3y -4.37 = 0$. Here $\dpi{100} a = 2, b = 3$and $\dpi{100} c = - 4.37$.

(ii)

The equation$\dpi{100} x - 4 = \sqrt{}3y$ can be written as  $\dpi{100} x -\sqrt{} 3y - 4 = 0$.  Here  $\dpi{100} a = 1,b =-\sqrt{}3$and $\dpi{100} c = -4$.

(iii) The equation

$\dpi{100} 5x -3y=4$ can be written as $\dpi{100} 5x -3y-4=0$. Here $\dpi{100} a = 5, b = -3$and $\dpi{100} c = - 4$ .

(iv) The equation

$\dpi{100} 2x = y$ can be written as $\dpi{100} 2x - y + 0 = 0$. Here $\dpi{100} a = 2, b = -1$ and $\dpi{100} c = 0$ .

## Topics of NCERT Grade 9 Maths Chapter 4 Linear Equations in Two Variables-

4.1 Introduction

4.2 Linear Equations

4.3 Solution of a Linear Equation

4.4 Graph of a Linear Equation in Two Variables

4.5 Equations of Lines Parallel to x-axis and y-axis

4.6 Summary

The complete Solutions of NCERT Class 9 Mathematics Chapter 4 is provided below:

## NCERT Solutions for Class 9 Maths - Chapter Wise

 Chapter No. Chapter Name Chapter 1 Number Systems Chapter 2 Polynomials Chapter 3 Coordinate Geometry Chapter 5 Introduction to Euclid's Geometry Chapter 6 Lines And Angles Chapter 7 Triangles Chapter 8 Quadrilaterals Chapter 9 Areas of Parallelograms and Triangles Chapter 10 Circles Chapter 11 Constructions Chapter 12 Heron’s Formula Chapter 13 Surface Area and Volumes Chapter 14 Statistics Chapter 15 Probability