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

Quizplus · Accepted Answer

The system of linear equations is:

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

From the third row, we can see that $z = 5$. Substituting this in the second equation gives $y + 4(5) = 19$, which simplifies to $y = -1$. Finally, substituting $z = 5$ and $y = -1$ in the first equation gives $x + 4(-1) - 3(5) = -23$, which simplifies to $x = -4$. Therefore, the solution is $x=-4$, $y=-1$, and $z=5$. So, the best choice is D.

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

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