Solving the system , we found a single solution: the ordered pair (3,5). So we say that the system is **possible** (has solution) and **determined** (single solution).

In the case of the system , we find that the ordered pairs (0.8), (1.7), (2.6), (3.5), (4.4), (5.3),… are some of their infinite solutions. Therefore, we say that the system is **possible** (has solution) and **undetermined** (infinite solutions).

For , we find that no ordered pair simultaneously satisfies the equations. Therefore, the system is **impossible** (there is no solution).

In short, a linear system can be:

a) possible and determined (single solution);

b) possible and undetermined (infinite solutions);

c) impossible (no solution).

## Normal system

A system is normal when it has the same number of equations (**m**) and unknowns (**no**) and the determinant of the incomplete matrix associated with the system is nonzero. If m = n and det A 0, so the system is normal.

## Cramer's Rule

Every normal system has a single solution given by:

where i {1,2,3,…, n}, D = det A is the determinant of the incomplete matrix associated with the system, and D_{xi }is the determinant obtained by substituting, in the incomplete matrix, the column **i **by the column formed by the independent terms.