Have been having problems with this equation system for a while, \begin{array}{l} x - y - az = 1\\ ax + y + az = a\\ ax + 3y + 3z = -1 \end{array} where I need to find all the values of $a\in \mathbb{R}$.
I have tried to solve the system with elimination, by subtracting the first line multiplied by $(-a)$ with the second and third line and so on. I have found $z$ to be $\frac{-1 -a}{3+3a}$ but after integrating it and solving for $y$ I'm lost.
Any help is appreciated, thanks in advance!
Hint: Adding equation 1 and 2, we get $$x(a+1)=a+1$$ so $$(a+1)(x-1)=0$$ Can you proceed?