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) $x = 1 , y = 5 , z = 4$

Question

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) $x = 1 , y = 5 , z = 4$

Quizplus · Accepted Answer

The augmented matrix represents the system of equations: $x + 4y - 3z = -23$, $y + 4z = 19$, and $z = 5$. Using back-substitution, substitute $z = 5$ into the second equation to find $y = -1$, and then substitute $y = -1$ and $z = 5$ into the first equation to find $x = -4$.

Write the System of Linear Equations Represented by the Augmented x,yx , yx,y

Write the System of Linear Equations Represented by the Augmented $x , y$