Supposing I had two equations: $\alpha/\beta=\mu$ and $\alpha/\beta^{2}=\sigma^{2}$, where $\alpha$, $\beta$, $\sigma$ and $\mu \in \mathbb R$. How can I solve for $\alpha$ and $\beta$?
Furthermore, is there a general method for this kind of system?
Supposing I had two equations: $\alpha/\beta=\mu$ and $\alpha/\beta^{2}=\sigma^{2}$, where $\alpha$, $\beta$, $\sigma$ and $\mu \in \mathbb R$. How can I solve for $\alpha$ and $\beta$?
Furthermore, is there a general method for this kind of system?
Solving one equation for $\alpha$ gives p. e. $\alpha = \beta\mu$. Plug this into the other equation, giving $\beta\mu/\beta^2 = \sigma^2 \iff \beta = \mu/\sigma^2$. So $\alpha = \mu^2/\sigma^2$.