For the system $\left\{ \begin{array} { l }
3 x + y + z = 0 \
x - 2 y + 5 z = 14 \
x + y - 5 z = - 12
\end{array} \right.$ , $D _ { x } = 0$ , $D _ { y } = - 56$ , and $D = 28$ . What is the solution of the system?
A) $\left( \frac { 1 } { 2 } , - \frac { 1 } { 2 } , 2 \right)$
B) $( 0,2,2 )$
C) $( 0 , - 2,2 )$
D) none of these

Question

For the system $\left\{ \begin{array} { l } 
3 x + y + z = 0 \
x - 2 y + 5 z = 14 \
x + y - 5 z = - 12
\end{array} \right.$ , $D _ { x } = 0$ , $D _ { y } = - 56$ , and $D = 28$ . What is the solution of the system?
A) $\left( \frac { 1 } { 2 } , - \frac { 1 } { 2 } , 2 \right)$
B) $( 0,2,2 )$
C) $( 0 , - 2,2 )$
D) none of these

Quizplus · Accepted Answer

The solution is found using Cramer's Rule. Since $D_x = 0$, $D_y = -56$, and $D = 28$, the solution for $y$ is $-56/28 = -2$. For $z$, since $D_z = 56$, $z = 56/28 = 2$. Since $D_x = 0$, $x = 0$. Thus, the solution is $(0, -2, 2)$.

For the System {3x+y+z=0x−2y+5z=14x+y−5z=−12\left\{ \begin{array} { l } 3 x + y + z = 0 \\x - 2 y + 5 z = 14 \\x + y - 5 z = - 12\end{array} \right.⎩⎨⎧​3x+y+z=0x−2y+5z=14x+y−5z=−12​

For the System $\left\{ \begin{array} { l } 3 x + y + z = 0 \\x - 2 y + 5 z = 14 \\x + y - 5 z = - 12\end{array} \right.$