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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.
| Author | NCERT |
| Language | English |
| No. of Pages | 12 |
| PDF Size | 116 KB |
| Category | Mathematics |
| Source/ Credits | ncert.nic.in |
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