Question

In general, a linear equation in three variables x,y,z has the form Ax+By+Cz=D (where A,B,C,D are some constants) and geometrically corresponds to a plane in 3D. Graphically, the solution of a system of two linear equations in three variables CANNOT be?

empty
a plane
one point
a line

Answer 1

one point

Explanation:

A linear equation in `3` variables represents a plane in 3 dimensional space.

So a system of two such equations represents two planes, with the solution being the points of intersection.

Two planes may be parallel, so not intersect, or cross in a line or be identical.

They cannot intersect at just one point.