memo for my low-memory brain: calculate intersection from two lines in 2-D.

This is my memo for basic geometry-formula.
Now, I want to calculate intersection of two lines(Line1 and Line2).

Line1: passes point (x1=0, y1=9) and (x2=2, y2=5).
Line2: passes point (x3=1, y3=1) and (x4=3, y4=0).

Firstly, we can express these lines as following:
Line1:
Line2:

Secondly, we can get intersection (x,y) by solving below linear algebra:










Finally, using inverse matrix, we can easily calculate intersection: