Inconsistent System of 3 Equations

[xxMsJojoxx]

I have the following system, which is supposed to be inconsistent.

However, when I graphed them, all 3 planes seem to be intersecting with one another. Or maybe I am not reading the graph correctly. Can you explain the graph more clearly to me? How can I tell that the system is inconsistent, from the graph?

Can we tell because the green plane is not touching the purple plaen, as the pink one is 'blocking' it?

 

[pka]

Have a look at this calculation. The determinate of the matrix of coefficients is zero.
That does that tell us about possible solutions?

 

[Dr.Peterson]

It appears that pairs of planes intersect in parallel lines that are very close at this scale. Probably if you zoom in you will see this more clearly.

Of course, in general you can't be sure whether a system is inconsistent from looking at a graph; but when you know it is, the graph can show why.

 

[JeffM]

These planes are not physical objects: there is no blocking possible. It's like ghosts that pass right through walls.

One way that such a system can be inconsistent is that two planes are parallel and never intersect. That is not the case here.

The other way is that the planes all intersect, but they do so on two parallel lines of intersection so that the two lines do not intersect in a point.

Dr. Peterson has explained that your graph is not detailed enough to see that. That is is one of the problems with graphical methods.