Ex.4.4 Q1 Linear Equations in Two Variables Solution - NCERT Maths Class 9
Give the geometric representation of \(y = 3\) as an equation
(i) in one variable
(ii) in two variables
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.
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 \(3.\)
- 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: