Find all solutions of the system. $$\left\{ \begin{array} { r }
x + y + z = 12 \
2 x - y - z = - 5 \
6 x + 2 y + z = 30
\end{array} \right.$$
A) $\left( \frac { 10 } { 3 } , \frac { 16 } { 3 } , \frac { 10 } { 3 } \right)$
B) $\left( 19 , \frac { 10 } { 3 } , \frac { 7 } { 3 } \right)$
C) $\left( \frac { 7 } { 3 } , \frac { 19 } { 3 } , \frac { 10 } { 3 } \right)$
D) $\text { The system is dependent. }$
E) $\text { The system is inconsistent. }$

Question

Find all solutions of the system. $$\left\{ \begin{array} { r } 
x + y + z = 12 \
2 x - y - z = - 5 \
6 x + 2 y + z = 30
\end{array} \right.$$
A) $\left( \frac { 10 } { 3 } , \frac { 16 } { 3 } , \frac { 10 } { 3 } \right)$
B) $\left( 19 , \frac { 10 } { 3 } , \frac { 7 } { 3 } \right)$
C) $\left( \frac { 7 } { 3 } , \frac { 19 } { 3 } , \frac { 10 } { 3 } \right)$
D) $\text { The system is dependent. }$
E) $\text { The system is inconsistent. }$

Quizplus · Accepted Answer

The Answer is C

Find All Solutions of the System {x+y+z=122x−y−z=−56x+2y+z=30\left\{ \begin{array} { r } x + y + z = 12 \\2 x - y - z = - 5 \\6 x + 2 y + z = 30\end{array} \right.⎩⎨⎧​x+y+z=122x−y−z=−56x+2y+z=30​

Find All Solutions of the System $\left\{ \begin{array} { r } x + y + z = 12 \\2 x - y - z = - 5 \\6 x + 2 y + z = 30\end{array} \right.$