Chapter 17.3, Problem 32E

To determine

To derive: The equations $\left({\displaystyle \sum x}\right)b+\left({\displaystyle \sum x^2}\right)m={\displaystyle \sum xy}$ and $nb+\left({\displaystyle \sum x}\right)m={\displaystyle \sum y}$ by equate partial derivative $S_m\left(m,b\right)=0$ and $S_b\left(m,b\right)=0$, where $S\left(m,b\right)={\displaystyle \sum {\left(mx+b-y\right)}^2}$.