Use back-substitution to solve the system of linear equations.? $$\left\{ \begin{array} { c c c }
4 x - 3 y - 2 z & = & 21 \
6 y - 5 z & = & 5 \
z & = & - 7
\end{array} \right.$$ ?
A)? $( - 2 , - 5 , - 7 )$
B)? $( - 2,5,7 )$
C)? $( - 5,7 , - 2 )$
D)? $( - 2 , - 5,7 )$
E)? $( - 5 , - 7 , - 2 )$

Question

Use back-substitution to solve the system of linear equations.? $$\left\{ \begin{array} { c c c } 
4 x - 3 y - 2 z & = & 21 \
6 y - 5 z & = & 5 \
z & = & - 7
\end{array} \right.$$ ?
A)? $( - 2 , - 5 , - 7 )$
B)? $( - 2,5,7 )$
C)? $( - 5,7 , - 2 )$
D)? $( - 2 , - 5,7 )$
E)? $( - 5 , - 7 , - 2 )$

Quizplus · Accepted Answer

Given $z = -7$, substitute $z$ into the second equation to find $y$: $6y - 5(-7) = 5 \Rightarrow 6y + 35 = 5 \Rightarrow 6y = -30 \Rightarrow y = -5$. Then, substitute $y$ and $z$ into the first equation to find $x$: $4x - 3(-5) - 2(-7) = 21 \Rightarrow 4x + 15 + 14 = 21 \Rightarrow 4x = -8 \Rightarrow x = -2$. Therefore, the solution is $(-2, -5, -7)$.

Use Back-Substitution to Solve the System of Linear Equations {4x−3y−2z=216y−5z=5z=−7\left\{ \begin{array} { c c c } 4 x - 3 y - 2 z & = & 21 \\6 y - 5 z & = & 5 \\z & = & - 7\end{array} \right.⎩⎨⎧​4x−3y−2z6y−5zz​===​215−7​

Use Back-Substitution to Solve the System of Linear Equations $\left\{ \begin{array} { c c c } 4 x - 3 y - 2 z & = & 21 \\6 y - 5 z & = & 5 \\z & = & - 7\end{array} \right.$