Answer
\begin{cases}
x+y+z=-3
\\
2x+y+z=-4
\\
x+2y+z=-1
\end{cases}
Work Step by Step
To find a system that has $(
-1,2,-4
)$ as a solution, make equations using the given points.
Since $
-1+2+(-4)=-3
,$ then $
x+y+z=-3
$ has the given point as a solution.
Since $
2(-1)+2+(-4)=-4
,$ then $
2x+y+z=-4
$ has the given point as a solution.
Since $
-1+2(2)+(-4)=-1
,$ then $
x+2y+z=-1
$ has the given point as a solution.
Hence, a system that has the given point as a solution is
\begin{cases}
x+y+z=-3
\\
2x+y+z=-4
\\
x+2y+z=-1
\end{cases}
