## Algebra and Trigonometry 10th Edition

Gaussian Elimination: $\begin{bmatrix} 3 & -2 & 1 & |15\\ -1 & 1 & 2 & |-10\\ 1 & -1 & -4 & |14\\ \end{bmatrix}$ ~ $\begin{bmatrix} 1 & -1 & -4 & |14\\ -1 & 1 & 2 & |-10\\ 3 & -2 & 1 & |15\\ \end{bmatrix}$ ~ $\begin{bmatrix} 1 & -1 & -4 & |14\\ 0 & 0 & -2 & |4\\ 0 & 1 & 13 & |-27\\ \end{bmatrix}$ ~ $\begin{bmatrix} 1 & -1 & -4 & |14\\ 0 & 1 & 13 & |-27\\ 0 & 0 & -2 & |4\\ \end{bmatrix}$ Back-Substitution: Z: -2z = 4 z = -2 Y: y + (-2)(13) = -27 y - 26 = -27 y = -1 X: x - (1)(-1) - 4(-2) = 14 x + 1 + 8 = 14 x + 9 = 14 x = 5 In Total: x = 5 y = -1 z = -2