# Ex.4.4 Q2 Linear Equations in Two Variables Solution - NCERT Maths Class 9

## Question

Give the geometric representations of

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

(i) in one variable

(ii) in two variables

## Text 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 \(4.5\)