Solve the system of linear equations.
$$\left\{ \begin{array} { c }
x + y + z + w = 3 \
- x - y + z + w = - 5 \
x + 3 z + w = - 6 \
- 4 x - 4 y - 2 z - w = - 13
\end{array} \right.$$
A) $( - 1,5,1 , - 2 )$
B) $( - 1 , - 2,5,1 )$
C) $( 1,5 , - 2 , - 1 )$
D) $( - 1,5 , - 2,1 )$
E) inconsistent

Question

Solve the system of linear equations.
$$\left\{ \begin{array} { c } 
x + y + z + w = 3 \
- x - y + z + w = - 5 \
x + 3 z + w = - 6 \
- 4 x - 4 y - 2 z - w = - 13
\end{array} \right.$$
A) $( - 1,5,1 , - 2 )$
B) $( - 1 , - 2,5,1 )$
C) $( 1,5 , - 2 , - 1 )$
D) $( - 1,5 , - 2,1 )$
E) inconsistent

Quizplus · Accepted Answer

To solve the system, we can use various methods such as substitution, elimination, or matrix methods. By substituting the given options into the equations, we find that option D $(-1, 5, -2, 1)$ satisfies all the equations, making it the correct solution.