Write the System of Linear Equations Represented by the Augmented $\left[\begin{array}{rrrrl}1 & 0 & 0 & 4 & :-5\\3 & -7 & 0 & 0 & :3\\0&-4&8&-1&:-6 \\0 & 0 & 3 & 7 &:7\end{array}\right]$

Multiple Choice

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

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) $$\left\{ \begin{aligned}x + 4 w & = - 5 \\3 x - 7 y & = 3 \\- 4 y + 8 z - w & = - 6 \\3 z + 7 w & = 7\end{aligned} \right.$$ ​