Solve the system.
-$\left\{ \begin{array} { r r }
x - 3 y - z = & - 5 \
5 x - 15 y - 5 z = & - 25 \
- 2 x + 6 y + 2 z = & 10
\end{array} \right.$
A) $( 5 , - 2,16 )$
B) $( - 2,5 , - 12 )$
C) $\{ ( x , y , z ) \mid x - 3 y - z = - 5 \}$
D) $\varnothing$

Question

Solve the system.
-$\left\{ \begin{array} { r r } 
x - 3 y - z = & - 5 \
5 x - 15 y - 5 z = & - 25 \
- 2 x + 6 y + 2 z = & 10
\end{array} \right.$
A) $( 5 , - 2,16 )$
B) $( - 2,5 , - 12 )$
C) $\{ ( x , y , z ) \mid x - 3 y - z = - 5 \}$
D) $\varnothing$

Quizplus · Accepted Answer

The system of equations is dependent, meaning all equations represent the same plane in three-dimensional space. This is evident because the second and third equations can be derived by multiplying the first equation by 5 and -2, respectively. Therefore, there are infinitely many solutions that satisfy the condition $x - 3y - z = -5$, not just a single point.

Solve the System {x−3y−z=−55x−15y−5z=−25−2x+6y+2z=10\left\{ \begin{array} { r r } x - 3 y - z = & - 5 \\5 x - 15 y - 5 z = & - 25 \\- 2 x + 6 y + 2 z = & 10\end{array} \right.⎩⎨⎧​x−3y−z=5x−15y−5z=−2x+6y+2z=​−5−2510​

Solve the System $\left\{ \begin{array} { r r } x - 3 y - z = & - 5 \\5 x - 15 y - 5 z = & - 25 \\- 2 x + 6 y + 2 z = & 10\end{array} \right.$