Write the System of Linear Equations Represented by the Augmented $$\left[ \begin{array} { c c c : c } 1 & 4 & - 3 & - 23 \\0 & 1 & 4 & 19 \\0 & 0 & 1 & 5\end{array} \right]$$

Multiple Choice

Write the system of linear equations represented by the augmented matrix. Then use back-substitution to solve. (Use variables x, y, and z.) $$\left[ \begin{array} { c c c : c } 1 & 4 & - 3 & - 23 \\0 & 1 & 4 & 19 \\0 & 0 & 1 & 5\end{array} \right]$$

A) $x = - 44 , y = 3 , z = - 3$
B) $x = - 1 , y = - 4 , z = 5$
C) $x = - 4 , y = 1 , z = - 5$
D) $x = - 4 , y = - 1 , z = 5$
E) $x = 1 , y = 5 , z = 4$