Chapter 1 - Systems of Linear Equations - 1.2 Gaussian Elimination and Gauss-Jordan Elimination - 1.2 Exercises - Page 23: 34

$x_1 = 1+2x_3$ $x_2 = 2+3x_3$ $x_3 = free$

$\begin{matrix}1&1&-5&3\\1&0&-2&1\\2&-1&-1&0\\\end{matrix}$ $-R_1 + R_2, -2R_1 +R_3$ $\begin{matrix}1&1&-5&3\\0&-1&3&-2\\0&-3&9&-6\\\end{matrix}$ $R_2 + R_1, -3_R2 +R_3$ $\begin{matrix}1&0&-2&1\\0&-1&3&-2\\0&0&18&0\\\end{matrix}$ $-R_2,1/18 R_3$ $\begin{matrix}1&0&-2&1\\0&1&-3&2\\0&0&1&0\\\end{matrix}$