Write the System of Linear Equations Represented by the Augmented

Multiple Choice

Write the system of linear equations represented by the augmented matrix.(Use variables x, y, z, and w.) $\left[ \begin{array} { r r r r r } 1&0&0&4 & \vdots&-5 \\3&-7&0&0 & \vdots & 3 \\0&-4&8&-1& \vdots &-6\\0&0&3&7 & \vdots &7\\\end{array} \right]$

A) $\left\{ \begin{array} { r l r } x + 4 y & = & - 5 \\3 x - 7 y & = & 3 \\- 4 x + 8 y - z & = & - 6 \\3 x + 7 y & = & 7\end{array} \right.$
B) $\left\{ \begin{array} { r l r } x + 4 z & = - 5 \\3 x - 7 y & = 3 \\- 4 y + 8 z - w & = - 6 \\3 z z + 7 w & = 7\end{array} \right.$
C) $\left\{ \begin{array} { r l r } x + 4 z & = - 5 \\3 x - 7 z & = 3 \\- 4 y + 8 z - w & = - 6 \\3 z z + 7 w & = 7\end{array} \right.$
D) $\left\{ \begin{array} { r l r } x - 4 w & = - 5 \\3 x - 7 y & = 3 \\- 4 y + 8 z - w & = - 6 \\3 y + 7 z & = 7\end{array} \right.$
E) $\left\{ \begin{aligned}x + 4 w & = - 5 \\3 x - 7 y & = 3 \\- 4 y + 8 z - w & = - 6 \\3 z + 7 w & = 7\end{aligned} \right.$