The coordinates of the point of intersection of the lines x = 1 and y = 1 are:

For any constant k, the line x = k is a vertical line containing every point whose x-coordinate equals k, for any value of y. Likewise, y = k is a horizontal line containing every point whose y-coordinate equals k, for any value of x. Two such lines meet where both conditions hold together, giving a unique point (x, y).

1. The line x = 1 is a vertical line, so its points are of the form (1, y) for every value of y.

2. The line y = 1 is a horizontal line, so its points are of the form (x, 1) for every value of x.

3. A point common to both lines must have x-coordinate 1 (from the first line) and y-coordinate 1 (from the second line) at the same time.

4. That common point is (1, 1).

Substituting (1, 1) back into both equations confirms it: the x-coordinate is 1, which satisfies x = 1, and the y-coordinate is 1, which satisfies y = 1, so (1, 1) is indeed the point of intersection.