I have to find MLE estimators of $\theta$ and $\sigma^{2}$. However, I could not solve these two equations. Do you have any idea about how to proceed?
$ \frac{-\theta}{1-\theta^{2}}+\frac{\theta}{\sigma^{2}}y_{1}^{2} + \frac{y_{1}}{\sigma^{2}}(y_{2}-\theta y_{1})=0 \\ \frac{-1}{\sigma^{2}}+\frac{1}{2\sigma^{4}}(1-\theta^2)y_{1}^2 + \frac{1}{2\sigma^4}(y_{2}-\theta y_{1})^2=0 $
Only $\theta$ and $\sigma^2$ are variables. The rest is constant.