Find all solutions of the system. $$\left\{ \begin{array} { l }
x + y + z + w = 4 \
x - 2 y - z - w = 6 \
2 x - y + z - w = 5 \
x - y + 2 z - 2 w = - 5
\end{array} \right.$$
A) $( 0 , - 2,4,5 )$
B) $( 5,0 , - 3,2 )$
C) $( - 8,2 , - 5,0 )$
D) $\text { The system is dependent. }$
E) $\text { The system is inconsistent. }$

Question

Find all solutions of the system. $$\left\{ \begin{array} { l } 
x + y + z + w = 4 \
x - 2 y - z - w = 6 \
2 x - y + z - w = 5 \
x - y + 2 z - 2 w = - 5
\end{array} \right.$$
A) $( 0 , - 2,4,5 )$
B) $( 5,0 , - 3,2 )$
C) $( - 8,2 , - 5,0 )$
D) $\text { The system is dependent. }$
E) $\text { The system is inconsistent. }$

Quizplus · Accepted Answer

To solve the system of equations, we can use methods such as substitution, elimination, or matrix operations. Without explicitly solving the system here, we can check each option by substituting the values of $x$, $y$, $z$, and $w$ into the original equations to see if they satisfy all the equations. Option B, $(5, 0, -3, 2)$, is the correct solution because when these values are substituted into each of the four equations, they satisfy all the equations, making the system consistent and the given option the correct solution.

Find All Solutions of the System {x+y+z+w=4x−2y−z−w=62x−y+z−w=5x−y+2z−2w=−5\left\{ \begin{array} { l } x + y + z + w = 4 \\x - 2 y - z - w = 6 \\2 x - y + z - w = 5 \\x - y + 2 z - 2 w = - 5\end{array} \right.⎩⎨⎧​x+y+z+w=4x−2y−z−w=62x−y+z−w=5x−y+2z−2w=−5​

Find All Solutions of the System $\left\{ \begin{array} { l } x + y + z + w = 4 \\x - 2 y - z - w = 6 \\2 x - y + z - w = 5 \\x - y + 2 z - 2 w = - 5\end{array} \right.$