# Linear Equations In Two Variables Chapter 4 Class 9 Maths NCERT PDF

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## NCERT Class 9 Maths Textbook Chapter 4 With Answer Book PDF Free Download

### Chapter 4: Linear Equations in Two Variables

#### 4.1 Introduction

In earlier classes, you have studied linear equations in one variable. Can you write down a linear equation in one variable?

You may say that x + 1 = 0, x + 2 = 0 and 2 y + 3 = 0 are examples of linear equations in one variable. You also know that such equations have a unique (i.e., one and only one) solution.

You may also remember how to represent the solution on a number line. In this chapter, the knowledge of linear equations in one variable shall be recalled and extended to that of two variables. You will be considering questions like:

Does a linear equation in two variables have a solution? If yes, is it unique?

What does the solution look like on the Cartesian plane? You shall also use the concepts you studied in Chapter 3 to answer these questions.

#### 4.2Linear Equations

Let us first recall what you have studied so far. Consider the following equation:
2x + 5 = 0
Its solution, i.e., the root of the equation, is 5 2
 . This can be represented on the number line as shown below:

#### 4.3 Solution of a Linear Equation

You have seen that every linear equation in one variable has a unique solution. What can you say about the solution of a linear equation involving two variables?

As there are two variables in the equation, a solution means a pair of values, one for x and one for y which satisfy the given equation.

Let us consider the equation 2x + 3y = 12. Here, x = 3 and y = 2 is a solution because when you substitute x = 3 and y = 2 in the equation above, you find that 2x + 3y = (2 × 3) + (3 × 2) = 12

This solution is written as an ordered pair (3, 2), first writing the value for x and then the value for y. Similarly, (0, 4) is also a solution for the equation above.

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

1. The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.

(Take the cost of a notebook to be ₹ x and that of a pen to be ₹ y)

Solution:

Let the cost of a notebook to be = ₹ x

Let the cost of a pen to be = ₹ y

According to the question,

The cost of a notebook is twice the cost of a pen.

i.e., Cost of a notebook = 2×Cost of a pen

x = 2×y

x = 2y

x-2y = 0

x-2y = 0 is the linear equation in two variables to represent the statement ‘The cost of a notebook is twice the cost of a pen’.

ii) x –(y/5)–10 = 0

Solution:

The equation x –(y/5)-10 = 0 can be written as,

1x+(-1/5)y +(–10) = 0

Now comparing x+(-1/5)y+(–10) = 0 with ax+by+c = 0

We get,

a = 1

b = -(1/5)

c = -10

(iii) –2x+3y = 6

Solution:

–2x+3y = 6

Re-arranging the equation, we get,

–2x+3y–6 = 0

The equation –2x+3y–6 = 0 can be written as,

(–2)x+3y+(– 6) = 0

Now comparing (–2)x+3y+(–6) = 0 with ax+by+c = 0

We get, a = –2

b = 3

c =-6

(iv) x = 3y

Solution:

x = 3y

Re-arranging the equation, we get,

x-3y = 0

The equation x-3y=0 can be written as,

1x+(-3)y+(0)c = 0

Now comparing 1x+(-3)y+(0)c = 0 with ax+by+c = 0

We get, a = 1

b = -3

c =0

(v) 2x = –5y

Solution:

2x = –5y

Re-arranging the equation, we get,

2x+5y = 0

The equation 2x+5y = 0 can be written as,

2x+5y+0 = 0

Now comparing 2x+5y+0= 0 with ax+by+c = 0

We get, a = 2

b = 5

c = 0

NCERT Class 9 Maths Textbook Chapter 4 With Answer Book PDF Free Download