Solve the system of linear equations. $$\left\{ \begin{array} { c l }
x + y + z + w & = - 1 \
- 2 x + y + 3 z - w & = 6 \
2 x + 2 z - 2 w & = - 18 \
2 x + 4 y - 4 z + w & = 5
\end{array} \right.$$
A) $( - 5,2 , - 1,3 )$
B) $( - 5,2,3 , - 1 )$
C) $( 3,2 , - 1 , - 5 )$
D)inconsistent
E) $( - 5 , - 1,2,3 )$

Question

Solve the system of linear equations.  $$\left\{ \begin{array} { c l } 
x + y + z + w & = - 1 \
- 2 x + y + 3 z - w & = 6 \
2 x + 2 z - 2 w & = - 18 \
2 x + 4 y - 4 z + w & = 5
\end{array} \right.$$
A)  $( - 5,2 , - 1,3 )$
B)  $( - 5,2,3 , - 1 )$
C)  $( 3,2 , - 1 , - 5 )$
D)inconsistent
E)  $( - 5 , - 1,2,3 )$

Quizplus · Accepted Answer

To solve the system of linear equations, we can use methods such as substitution, elimination, or matrix operations. Without explicitly solving the system step by step, 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 equations. Option A $(-5, 2, -1, 3)$ 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 solvable with this specific solution.

Solve the System of Linear Equations A) (−5,2,−1,3)( - 5,2 , - 1,3 )(−5,2,−1,3)

Solve the System of Linear Equations A) $( - 5,2 , - 1,3 )$