I used a graphical package to draw these 3 pairs of curves on the same set of axes:

$x + y -1 =0\quad\mbox{and}\quad (x+y-1)(x^2+y^2)=0$

$x + y = 0\quad\mbox{and}\quad (x + y)(y^2+(x+1)^2)=0$

$x + y = 1\quad\mbox{and}\quad x^3 + 3xy + y^3 = 1$




Can you explain what has happened? Can you work out which curves go with which lines? Are there any points missing from the graphs? If so, where should these be?


Can you think of any others sets of curves which might fool the computer?