When its matrix is non-singular.
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yes it can . the system may have infinitely many solutions.
A system of linear equations that has at least one solution is called consistent.
No....not necessary
Yes
A system of linear equations is consistent if there is only one solution for the system. Thus, if you see that the drawn lines intersect, you can say that the system is consistent, and the point of intersection is the only solution for the system. A system of linear equations is inconsistent if it does not have any solution. Thus, if you see that the drawn lines are parallel, you can say that the system is inconsistent, and there is not any solution for the system.