Solve the equation $2x + 1 = x -3$, and represent the solution(s) on

$(i)$ the number line,

$(ii)$ the Cartesian plane.

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

$x+0 y=-\,4$

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 $0y$ is always $0 .$ However, $x$ must satisfy the equation $x=-4 .$ Hence, two solutions of the given equation are $x=-4$, $y=0$ and $x=-\,4$ $y=2$

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) $).

Similarly, you can obtain a line parallel to the $x$ - axis corresponding to equations of the type

$y=3$   or    $0x+1y=3$