Use back-substitution to solve the system of linear equations. ?? $$\left\{ \begin{array} { c l }
2 x - y + 5 z & = 24 \
y + 2 z & = 9 \
z & = 7
\end{array} \right.$$ ?
A)? $$( - 8 , - 5,7 )$$
B)?? $$( - 8,5,7 )$$
C)?? $( - 8 , - 5 , - 7 )$
D)?? $( - 7 , - 5,7 )$
E)?? $( - 8 , - 5 , - 5 )$

Question

Use back-substitution to solve the system of linear equations. ?? $$\left\{ \begin{array} { c l } 
2 x - y + 5 z & = 24 \
y + 2 z & = 9 \
z & = 7
\end{array} \right.$$ ?
A)? $$( - 8 , - 5,7 )$$
B)?? $$( - 8,5,7 )$$
C)?? $( - 8 , - 5 , - 7 )$
D)?? $( - 7 , - 5,7 )$
E)?? $( - 8 , - 5 , - 5 )$

Quizplus · Accepted Answer

Starting with $z = 7$, we substitute this into the second equation to find $y$: $y + 2(7) = 9$, so $y = 9 - 14 = -5$. Then, substituting $y = -5$ and $z = 7$ into the first equation: $2x - (-5) + 5(7) = 24$, we solve for $x$: $2x + 5 + 35 = 24$, thus $2x = -16$, and $x = -8$. Therefore, the solution is $(-8, -5, 7)$.

Use Back-Substitution to Solve the System of Linear Equations {2x−y+5z=24y+2z=9z=7\left\{ \begin{array} { c l } 2 x - y + 5 z & = 24 \\y + 2 z & = 9 \\z & = 7\end{array} \right.⎩⎨⎧​2x−y+5zy+2zz​=24=9=7​

Use Back-Substitution to Solve the System of Linear Equations $\left\{ \begin{array} { c l } 2 x - y + 5 z & = 24 \\y + 2 z & = 9 \\z & = 7\end{array} \right.$