## Algebra and Trigonometry 10th Edition

$\begin{bmatrix} 3 & 2 & -1 & 1 & |0\\ 1 & -1 & 4 & 2 & |25\\ -2 & 1 & 2 & -1 & |2\\ 1 & 1 & 1 & 1 & |6\\ \end{bmatrix}$ ~ $\begin{bmatrix} 1 & 1 & 1 & 1 & |6\\ 1 & -1 & 4 & 2 & |25\\ -2 & 1 & 2 & -1 & |2\\ 3 & 2 & -1 & 1 & |0\\ \end{bmatrix}$ ~ $\begin{bmatrix} 1 & 1 & 1 & 1 & |6\\ 0 & 2 & -3 & -1 & |-19\\ 0 & 3 & 4 & 1 & |14\\ 0 & -1 & -4 & -2 & |-18\\ \end{bmatrix}$ ~ $\begin{bmatrix} 1 & 1 & 1 & 1 & |6\\ 0 & -1 & -4 & -2 & |-18\\ 0 & 3 & 4 & 1 & |14\\ 0 & 2 & -3 & -1 & |-19\\ \end{bmatrix}$ ~ $\begin{bmatrix} 1 & 1 & 1 & 1 & |6\\ 0 & -1 & -4 & -2 & |-18\\ 0 & 0 & -8 & -5 & |-40\\ 0 & 0 & -11 & -5 & |-55\\ \end{bmatrix}$ Back-Substitution: Z: $8z + 5w = 40$ $\underline{-11z - 5w = -55}$ -3z = -15 z = 5 W: -8(5) - 5w = -40 -40 - 5w = -40 -5w = 0 w = 0 Y: -y - 4(5) - 2(0) = -18 -y - 20 = -18 -y = 2 y = -2 X: x - 2 + 5 + 0 = 6 x + 3 = 6 x = 3 In Total: x = 3 y = -2 z = 5 w = 0