Solving system of equations, (2 equations 3 variables)

linear-algebra systems-of-equations

I am a bit puzzled. Trying to solve this system of equations:

\begin{align*} -x + 2y + z=0\\ x+2y+3z=0\\ \end{align*}

The solution should be \begin{align*} x=-z\\ y=-z\\ \end{align*}

I just don't get the same solution. Please advice.


adding both equations we get $$y=-z$$ plugging this in the first equation we get $$-x-2z+z=0$$ tgherefore $$x=-z$$

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