The system of linear equations

Ohas 0 solutions
Ohas exactly 1 solution
Ohas infinitely many solutions

The given system of equations has three equations but is missing a closing statement for the second and third equations. However, if we analyze the structure, for a system to have more than one solution but a finite number, the equations must represent planes that overlap along a line. If they define consistent planes but are not parallel or identical, it can lead to infinitely many solutions; thus, misalignments can occur without contradictions.

To determine the precise nature of the solutions, it’s essential to fully define all the equations. Complete specification will allow for the use of techniques like substitution or matrix methods, making it easier to see if the equations indeed intersect in a consistent manner that leads to a finite number of solutions.