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 system of linear equations represented by the given augmented matrix is:

\begin{align*}
x+4y-3z&=-23 \
y+4z&=19 \
z&=5
\end{align*}

Using back-substitution, we can start by solving for $z=5$ in the third equation. Substituting this value of $z$ into the second equation, we get:

\begin{align*}
y+4(5)&=19 \
y+20&=19 \
y&=-1
\end{align*}

Finally, substituting $z=5$ and $y=-1$ into the first equation, we get:

\begin{align*}
x+4(-1)-3(5)&=-23 \
x-4-15&=-23 \
x&=-4
\end{align*}

Therefore, the solution to the system of linear equations is $x=-4$, $y=-1$, and $z=5$. The best choice is D.

Write the System of Linear Equations Represented by the Augmented [14−3−23014190015]\left[ \begin{array} { c c c : c } 1 & 4 & - 3 & - 23 \\0 & 1 & 4 & 19 \\0 & 0 & 1 & 5\end{array} \right]​100​410​−341​−23195​​

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