quality:corruption, stylistic:style_transfer, structural:scholar_edition, information:extraction
Given two line equations

The x and y coordinates of the point of intersection of two non-vertical lines can easily be found using the following substitutions and rearrangements.

Suppose that two lines have the equations y = ax + c and y = bx + d where a and b are the slopes (gradients) of the lines and where c and d are the y -intercepts of the lines. At the point where the two lines intersect (if they do), both y coordinates will be the same, hence the following equality:

We can rearrange this expression in order to extract the value of x,

and so,

To find the y coordinate, all we need to do is substitute the value of x into either one of the two line equations, for example, into the first:

Hence, the point of intersection is

Note that if a = b then the two lines are parallel and they do not intersect, unless c = d as well, in which case the lines are coincident and they intersect at every point.