Solve the equation $2x + 1 = x - 3$,and represent the solution$(s)$ on
$(i)$ the number line,
$(ii)$ the Cartesian plane.

(N/A) We solve $2x + 1 = x - 3$,to get
$2x - x = -3 - 1$
i.e.,$x = -4$
$(i)$ The representation of the solution on the number line is shown in Fig. $(i)$,where $x = -4$ is treated as an equation in one variable.
$(ii)$ We know that $x = -4$ can be written as
$x + 0y = -4$
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 $0y$ is always $0$. However,$x$ must satisfy the equation $x = -4$. Hence,two solutions of the given equation are $(-4, 0)$ and $(-4, 2)$.
Note that the graph $AB$ is a line parallel to the $y$-axis and at a distance of $4$ units to the left of it (see Fig. $(ii)$).