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.

Hint: multiplying the first equation by $-2$ and addin g to the second we get
$$6y-7z=2$$ (I)
multiplying the first by $-4$ and adding to the third we get
$$7y-7z=2$$ (II)
can yuo finish?
multiplying (I) by $-1$ and adding to (II):
we get $$y=0$$ and $$z=-\frac{2}{7}$$
i have got $$x=\frac{13}{7}$$ Make a Control if my solution is right
