Point of intersection of two lines

We know that the point of intersection fits for both equations. With the combination of these two equations we can calculate the coordinates.

Let the point of intersection's coordinates x0  and  y0 :

Multiply the second equation by (c1/c2) to get c1 in both equations:

Subtract this equation from the first equation:

Multiply this equation by (c2) to clear denominators:

Rearrange the equation to make the „y0” variant the subject of the formula:

Subtitute this expression of „y0” variant into the first equation:

Multiply both side of the equation with (b1 c2-b2 c1) to clear denominators:

Divide this expression by the common factor which is c1:

Rearrange this equation to make the „x0” variant the subject of the formula:

Subtitute this to the get „y0” expression: