Adding 'z' to 2D graph equation

[pairofstrings]

TL;DR Summary

2D equation:
$x^2 y^2 + x^2 y + x y =1$

Hi.
If I write any random equation in 2D then the graph undoubtedly shows up on that 2D graphing system.
Equation example: $x^2 y^2 + x^2 y + x y =1$

My question is: if I take the same equation: $x^2 y^2 + x^2 y + x y =1$ and if I manipulate the equation by including another variable $'z'$ in the equation like this: $x^2 y^2 z+ x^2 y z^2+ x y z =1$ then why is the 3D graph not showing up on that 3D graphing system?

Thanks.

 

[BvU]

then the graph undoubtedly shows up on that 2D graphing system

What are you talking about ? What 2D graphing system ? Any visual examples ?

then why is the 3D graph not showing up on that 3D graphing system?

Perhaps because "that" system has no telepathic capabilities ? What so you expect to see ?

$\$

 

[renormalize]

why is the 3D graph not showing up on that 3D graphing system?

BvU is right: you need to specify what "graphing system" you're asking about.

For example, Mathematica's ContourPlot and ContourPlot3D easily handle your 2D and 3D examples:

 

[pairofstrings]

Hi.
Sorry for not using math words. By saying 2D and 3D graphing system I mean 2D and 3D coordinate system.

In GeoGebra when I write random equation: $x^2y^2z+x^2yz^2+xyz=1$ I am getting a blank graph and sometimes like this (vertical axis is y-axis):

My question is that, is it possible to draw a 3D graph of any random 3D equation like the equation: $x^2y^2z+x^2yz^2+xyz=1$? If yes, then I will use a different 3D graphing software.