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.

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. 
