System of Equations: Is Solutions Infinite?

[phymatter]

if in a system of linear equations we have lesser number of linear equations than the number of variables then is the number of solutions set to the system always infinite ?

 

[Mark44]

Not necessarily.

For example, in this system the solution set is empty.
x + y + z = 2
x + y + z = 3

Geomatrically, this system represents two planes in three-dimensional space. The planes are parallel and don't intersect.