You have studied how to write the coordinates of a given point in the Cartesian plane.
Do you know where the points `(2, 0), (–3, 0), (4, 0)` and `(n, 0)`, for any real number n, lie in the Cartesian plane? Yes, they all lie on the x-axis. But do you know why? Because on the x-axis, the y-coordinate of each point is `0`.
In fact, every point on the x-axis is of the form `(x, 0)`. Can you now guess the equation of the x-axis? It is given by `y = 0`. Note that `y = 0` can be expressed as `0.x + 1.y = 0`. Similarly, observe that the equation of the y-axis is given by `x = 0`.
Now, consider the equation `x – 2 = 0`. If this is treated as an equation in one variable x only, then it has the unique solution `x = 2`, which is a point on the number line. However, when treated as an equation in two variables, it can be expressed as
`x + 0.y – 2 = 0`. This has infinitely many solutions. In fact, they are all of the form `(2, r)`, where `r` is any real number. Also, you can check that every point of the form (2, r) is a solution of this equation.
So as, an equation in two variables, `x – 2 = 0` is represented by the line AB in the graph in Fig. 4.8.