$$\left\{ \begin{matrix} \frac{\partial S(b0,\ b1)}{\partial b_{0}\ } = \ \frac{\partial(\sum_{i = 1}^{n}(\ y\text{i\ } - \text{\ b}0\ - \ b1\text{\ x}\text{i\ }\ )^{2})}{\partial b_{0}} = \ - 2\sum_{i = 1}^{n}(\ y\text{i\ } - \text{\ b}0\ - \ b1\text{\ x}\text{i\ }) = 0 \\ \frac{\partial S(b0,\ b1)}{\partial b_{1}} = \ \frac{\partial(\sum_{i = 1}^{n}(\ y\text{i\ } - \text{\ b}0\ - \ b1\text{\ x}\text{i\ }\ )^{2})}{\partial b_{1}} = \ - 2\sum_{i = 1}^{n}{x_{i}(}\ y\text{i\ } - \text{\ b}0\ - \ b1\text{\ x}\text{i\ }) = 0 \\ \end{matrix} \right.\ $$

$$\left\{ \begin{matrix} \sum_{i = 1}^{n}{yi - nb_{0} - b1\sum_{i = 1}^{n}{x\text{i\ } = 0}} \\ \sum_{i = 1}^{n}{xiyi - b_{0}\sum_{i = 1}^{n}{xi} - b1\sum_{i = 1}^{n}{x_{i}^{2} = 0}} \\ \end{matrix} \right.\ $$