Chapter 1.2, Problem 11E

Given the linear systems

(i) $\begin{array}{l}{x}_1+2x_2=2\\ 3x_1+7x_2=8\end{array}$   (ii) $\begin{array}{l}{x}_1+2x_2=1\\ 3x_1+7x_2=7\end{array}$

solve both systems by incorporating the right−hand sides into a $2\times 2$matrix B and computing the reduced row echelon form of

$(A|B)=\left[\begin{array}{cc}1& 2\\ 3& 7\end{array}|\begin{array}{cc}2& 1\\ 8& 7\end{array}\right]$