I've being studying projective geometry for a few days. One of the key aspect of this geometry is that any pair of lines always intersects at some unique point. For instance, the lines $2x + y = 0$ and $4x + 2y + 1 = 0$ of $\mathbb{RP}^2$ intersects at a unique point with homogeneous coordinates $[2:1:0]\times[4:2:1]=[1:-2:0]$. My question is the following : do we also have this property in affine geometry, i.e. does any par of lines always intersects at some unique point in affine geometry?
I can guess the answer would be no but I would not be able to justify it correctly. After working with these two geometries for a few days I still fail to see the differences between them. Any help would be much appreciated.