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
2 Answers
Sep 22, 2017
A point.
Explanation:
The graphical "solution" is the intersection of the two planes. A "solution" would imply that it isn't "empty" to me, but that would be a possible outcome of the equations. It could also be a plane, if the two functions are in fact identical. Most commonly, a realistic solution is the line defined by the intersection of one plane through another.
Sep 22, 2017
a plane
Explanation:
The solution of two lines in
is given by the solutions for
Also
and also they can be non intersecting.
The answer is a plane