Q:

How to tell the number of solutions to a simultaeneous equation?

How many solutions are there to the following simultaeneous equations?:
  $$
\begin{align}
x - 2y + 3z = 1\\
2x + 2y - z = 4\\
4x - y + 5z = 6
\end{align}
$$

How can I know the number of solutions that there are?
EDIT: 
I have found z = 0, y = 2/7, x = 11/7 as solutions but the answers I have say that there are infinite solutions. How can one deduce this?
Please note that I am a high school student and am unable to understand advanced mathematics.

A:

Find the augmented matrix corresponding to the system of equations, then, using Gaussian elimination, manipulate it into row echelon form. This will give you information about the number of solutions. 

