Or search by topic
Chieh Lung from Kolej Tuanku Jaafar school made a good start on this:
$x + y -1 =0$ and $x + y = 1$ are the same equation, they give the top line, running through $(1,0),(0.5,0.5)$ and $(0,1)$.$(x+y-1)(x^2+y^2)=0$. The solutions of this are like solving a quadratic equation, when solutions are when at least one of the brackets is equal to zero. Here the first bracket is the top line, and the second only has solutions at $(0,0)$ as we are in the real numbers.
$x^3 + 3xy + y^3 = 1$. This must also be a product of the lines and points. But I cannot find them.
Good start Chieh, Adam finished off your working;
This effect could be created many times by choosing two lines, and then multiplying them by points (say $x^2+y^2=0$).