# Another Look at Systems of Equations: Possible Solutions

This is more of a general question than a specific problem. While doing homework, I am being asked to find the solutions for complicated systems of equations, and I was wondering:

Suppose I were to be given 3 equations involving variables a, b, and c. The goal of the problem is to find the number of solutions (they do not necessarily have to be real) for the system of equations. Would it be more logical to use Cramer's Rule to solve the linear system or to use basic algebra? A roadmap of the following example problem or the like would be helpful.

A basic system taken from the book would be:

3a + 4y - z = 4
3a + 2b - 11c = -13
a + 2b + 3c = 7