Solve the system of linear equations.
$$\left\{ \begin{aligned}
x + y + z + w & = 11 \
- 2 x - y - 3 z + 4 w & = - 5 \
- 2 x - 5 z - w & = - 23 \
3 x + 5 y + z - 2 w & = 16
\end{aligned} \right.$$
A) $( 5,1,3,2 )$
B) $( 5,2,1,3 )$
C) $( 3,1,2,5 )$
D) $( 5,1,2,3 )$
E) inconsistent

Question

Quizplus · Accepted Answer

To solve the system of linear equations, we can use methods such as substitution, elimination, or matrix operations. Without going through the detailed steps due to the complexity of the system, 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 D $(5, 1, 2, 3)$ is the correct choice because when $x = 5, y = 1, z = 2,$ and $w = 3$ are substituted into each equation, all the equations are satisfied:1. $5 + 1 + 2 + 3 = 11$2. $-2(5) - 1 - 3(2) + 4(3) = -10 - 1 - 6 + 12 = -5$3. $-2(5) - 5(2) - 3 = -10 - 10 - 3 = -23$4. $3(5) + 5(1) + 2 - 2(3) = 15 + 5 + 2 - 6 = 16$

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

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