Question

Describe a situation in 3-dimensional space where a system of equations is inconsistent.

Answer 1

In 3D space, we have 3 variables. The standard is to go with x, y, z.

Consider these two equations

x+y+z = 10

x+y+z = 20

Those two equations are inconsistent. Why? We could replace each "x+y+z" with another variable, say the letter w, to get these two corresponding equations:

w = 10

w = 20

At this point, we can clearly see the contradiction. A variable cannot equal two different things at the same time.

In terms of a visual sense, the two original equations plot out parallel planes that never intersect.