Solve the equation

2x + 1 = x – 3, and represent the solution(s) on

(i) the number line,

(ii) the Cartesian plane.

Solving the given equation 2x + 1 = x – 3,

We have 2x – x = – 3 – 1

Or, x = – 4

(i) The representation of the solution on the number line is as shown:

x = – 4 is treated as an equation in one variable.

(ii) Equation x = – 4 is same as

x + 0.y = – 4

which is a linear equation in the variables x and y.

This is represented by a line. Now all the values of y are

permissible because 0.y is always 0. However, x must satisfy the

equation x = – 4.

The permissible values of x and y can be tabulated as:

Plotting the above values: