# Math Help - discussion about the resolution of a system

1. ## discussion about the resolution of a system

Hello I have an exercise of algebra it says to solve the system (S) below, but the prof told us that he had discussed depending on the values of :

I have wanted to calculate the determinant following :

If , the system is said "of Cramer" and like the system is homogeneous :

the only solution is

But what for ?

2. If a system is homogeneous and $\Delta= 0$, then there exist an infinite number of solutions.

3. We have :

so there are 4 cases to study :

is this what people expect me to do that :