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, you can use methods such as substitution, elimination, or matrix methods (like Gaussian elimination or using the inverse of the coefficient matrix). Without going through all the algebraic steps due to the complexity and length, the correct solution can be verified by substituting the values of $x, y, z,$ and $w$ from each option back into the original equations. Option A, $(-5, 2, -1, 3)$, satisfies all four equations, making it the correct choice.

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) $( - 5,2 , - 1,3 )$