2-D Color Solver
3 Blue 1 Brown has a sweet video about solving 2D equations (which also has a nice graphical explanation of solving 1 variable equations).
In this applet, the color is determined by the angle of the output with the origin, with the positive x-axis as red, and the point gets darker the larger the magnitude of the output.
So what do solutions of f(x,y)=0 look like?