Question

Give the geometrical representation of \[2x + 1 = x - 3\] as an equation
i) In one variable
ii) In two variables

Answer 1

Hint: Here we will first simplify the given equation and find the value of x and then represent it on the number line for one variable and for two variables we will represent it on the Cartesian plane.

Complete step-by-step answer:
(i) The given equation is:-
\[2x + 1 = x - 3\]
Simplifying it further we get:-
\[2x - x = - 3 - 1\]
Solving it further we get:-
\[x = - 4\]
Hence in variable the equation is \[x = - 4\].
Now in order to represent it geometrically we need to draw a number line representing \[x = - 4\].

(ii) The given equation is: -
\[2x + 1 = x - 3\]
Simplifying it further we get:-
\[2x - x = - 3 - 1\]
Solving it further we get:-
\[x = - 4\]
This implies, \[y = 0\]
Therefore, the equation in two variables is given by:-
\[x + 0y = - 4\]
Hence we get the point as \[\left( { - 4,0} \right)\] on the Cartesian plane.
Hence, representing this point on Cartesian plane we get:-

Note: Geometrical representation is the way of representing a line or a point on a number line or a graph. It involves plotting the points on the plane. While representing a line on a graph we need to find two points from which the line is passing and plot those points on the graph and finally join the points to get the line on the graph.
We can plot various figures like, parabola, ellipse, circles etc.
Also, students should keep a note while representing a linear equation in one variable we need to use a number line but when representing the equation in two variables we need to use the Cartesian plane.