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
empty
a plane
one point
a line
1 Answer
Sep 24, 2017
one point
Explanation:
A linear equation in
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.