Exercise E4.4 Linear Equations in Two Variables NCERT Solutions Class 9

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Chapter 4 Ex.4.4 Question 1

Give the geometric representation of \(y = 3\) as an equation

(i) in one variable

(ii) in two variables

Solution

Video Solution
  

Steps:

(i) Given,

Considering \(y = 3\) is the equation in one variable

The representation of the solution on the number when \(y = 3\) is treated as an equation in one variable

In one variable, \(y = 3\) represents a point as shown in following figure.

(ii) Given:

Considering \(y = 3\) is the equation in two variables

We know that \(y = 3\) can be written as \(0.x + y = 0\).

In two variables, \(y = 3\) represents a straight line passing through point \((0, 3)\) and parallel to \(x\)-axis. It is a collection of all the points on the plane, having their \(y\)-coordinate as \(3.\)

Hence,

  • When, \(x = 0\), we get \(y = 3\);
  • When \(x = 2\), we get \(y = 3\);
  • When \(x = -2\), we get \(y = 3\) are the solutions for the equations.

Plotting the points \((0, 3) (2, 3)\) and \((–2, 3)\) and on joining them we get the graph \(AB\) as a line parallel to \(x\)-axis at a distance of \(3\,\rm units\) above it

The graphical representation is shown below:

Chapter 4 Ex.4.4 Question 2

Give the geometric representations of

\(2x + 9 = 0\) as an equation

(i) in one variable

(ii) in two variables

Solution

Video Solution
 

Steps:

(i) Given: \(2x + 9 = 0\) is the Linear Equation -------- Equation (1)

\(\begin{align} 2 x + 9 &= 0 \\ 2 x &= - 9 \\ x &= \frac { - 9 } { 2 } \\ &= -4.5 \end{align}\)

Hence, in one variable \(2x + 9 = 0\) represents a point as shown in the following figure.

(ii) Given: \(2x + 9 = 0\) is the Linear Equation ------- Equation (1)

We know that \(2x + 9 = 0\) can be written as \(2x + 0y + 9 = 0\) as a linear equation in variables \(x\) and \(y\).

Value of \(y\) is always \(0\). However, \(x\) must satisfy the relation \(2x + 9= 0\)

\(\begin{align} \text { i.e. } \;\;\; x &= \frac { - 9 } { 2 } \\ & = - 4.5 \end{align}\)

Hence,

  • When, \(y= 0\), we get \(x= -4.5\);
  • When \(y = 2\), we get \(x= -4.5\);
  • When \(y = - 2\), we get \(x= -4.5\) are the solutions for the equations.

Hence three solution of the given equation are,

\(y = 0\); \(y = 2\) and \(y =\, – 2\).

Therefore, plotting the point and on joining them we get the graph \(AB\) as a line parallel to \(y\)-axis at a distance of on the left of \(y\)-axis It is a collection of all points of the plane, having their \(x\)-coordinate as \(4.5\)

  
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