$\left\{ \begin{aligned}
4 x + 2 z + w & = - 18 \
- x + y + 2 z - w & = 4 \
4 x - y + 2 w & = - 21 \
y + 4 z - w & = - 3
\end{aligned} \right.$
A) x=5, y=3, z=-1, w=-1
B) x=-10, y=0, z=-2, w=1
C) x=0, y=-5, z=1, w=5
D) x=-5, y=1, z=-1, w=0

Question

$\left\{ \begin{aligned}
4 x + 2 z + w & = - 18 \
- x + y + 2 z - w & = 4 \
4 x - y + 2 w & = - 21 \
y + 4 z - w & = - 3
\end{aligned} \right.$
A)  x=5, y=3, z=-1, w=-1 
B)  x=-10, y=0, z=-2, w=1 
C)  x=0, y=-5, z=1, w=5 
D)  x=-5, y=1, z=-1, w=0

Quizplus · Accepted Answer

Substituting x=-5, y=1, z=-1, w=0 into each equation satisfies all four equations.

{4x+2z+w=−18−x+y+2z−w=44x−y+2w=−21y+4z−w=−3\left\{ \begin{aligned}4 x + 2 z + w & = - 18 \\- x + y + 2 z - w & = 4 \\4 x - y + 2 w & = - 21 \\y + 4 z - w & = - 3\end{aligned} \right.⎩⎨⎧​4x+2z+w−x+y+2z−w4x−y+2wy+4z−w​=−18=4=−21=−3​

$\left\{ \begin{aligned}4 x + 2 z + w & = - 18 \\- x + y + 2 z - w & = 4 \\4 x - y + 2 w & = - 21 \\y + 4 z - w & = - 3\end{aligned} \right.$