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

Given $z = 7$, substituting into the second equation gives $y + 2(7) = 9$, so $y = 9 - 14 = -5$. Substituting $y = -5$ and $z = 7$ into the first equation gives $2x - (-5) + 5(7) = 24$, leading to $2x + 5 + 35 = 24$, so $2x = -16$, and $x = -8$. Thus, 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 $\left\{ \begin{array} { c l } 2 x - y + 5 z & = 24 \\y + 2 z & = 9 \\z & = 7\end{array} \right.$