\begin{align*} x - \alpha y &= 1\\ \alpha x - y &= 1 \end{align*}
For which values of alpha does the system have an infinite number of solutions, no solutions and one solution.
Find the solution when it is unique.
My attempt:
$-\alpha \cdot \mathrm{eqn}_1 + \mathrm{eqn}_2$ resulting in $(\alpha^2 - 1)y = 1-\alpha$.
then we get $y = (1-\alpha)/(\alpha^2-1)$
so, $y = -1/(1+\alpha)$, but I am trying to proceed