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NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables Ex 4.4

NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables Ex 4.4 are part of NCERT Solutions for Class 9 Maths. Here we have given NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables Ex 4.4.

Board CBSE
Textbook NCERT
Class Class 9
Subject Maths
Chapter Chapter 4
Chapter Name Linear Equations in Two Variables
Exercise  Ex 4.4
Number of Questions Solved 2
Category NCERT Solutions

NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables Ex 4.4

Ex 4.4 Class 9 Maths Question 1.
Give the geometric representations of y – 3 as an equation
(i) in one variable.
(ii) in two variables.
Solution:
The given linear equation is
y = 3 …(i)
(i) The representation of the solution on the number line is shown in the figure below, where y = 3 is treated as an equation in one variable.
NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables Ex 4.4.1

(ii) We know that y = 3 can be written as
0. x + y = 3
Which is a linear equation in the variables x and y. This is represented by a line. Now, all the values of x are permissible because 0.x is always 0. However, y must satisfy the equation y = 3.
Note that, the graph AB is a line parallel to the x-axis and at a distance of 3 units of the upper side of it.
NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables Ex 4.4.2

Ex 4.4 Class 9 Maths Question 2.
Give the geometric representations of 2x + 9 = 0 as an equation
(i) in one variable
(ii) in two variables
Solution:
Given linear equation is 2x + 9 = 0 i.e., x = – \cfrac { 9 }{ 2 }
(i) If x = – \cfrac { 9 }{ 2 } is treated as an equation in one variable, then it has a unique
solution x = – \cfrac { 9 }{ 2 } .
So, it is a point on the number line as shown below :
NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables Ex 4.4.3

(ii) Given equation 2x + 9 = 0 can be written as 2x + 0 . y + 9 = 0, which is a linear equation in two variables x and y.
We can write the given equation as,
x=\cfrac { -9+0.y }{ 2 }
When y=1, then x=\cfrac { -9+0.(1) }{ 2 } = – \frac { 9 }{ 2 }
When y=2, then x=\cfrac { -9+0.(2) }{ 2 } = – \frac { 9 }{ 2 }
When y=3, then x=\cfrac { -9+0.(3) }{ 2 } = – \frac { 9 }{ 2 }

X – \frac { 9 }{ 2 } – \frac { 9 }{ 2 } – \frac { 9 }{ 2 }
y 1 2 3

Now Playing the points – (\cfrac { 9 }{ 2 },1 ), – (\cfrac { 9 }{ 2 },2 ) – (\cfrac { 9 }{ 2 },3 ) paper and joining then ,we get a line PQ as a solution of 2x+9=0
NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables Ex 4.4.4
Thus, the graph PQ is a line parallel to the y-axis at a distance \frac { 9 }{ 2 }=4.5 of units in the direction of negative X-axis.

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