Answer
equations a, c, d
Work Step by Step
Substituting the given point $
(2,1,-4)
,$ in the choices results to
\begin{array}{l}\require{cancel}
\text{a. }\\
x+y+z=-1
\\\\
2+1+-4=-1
\\\\
-1=-1
\text{ (TRUE)}
\\\\
\text{b. }\\
x-y-z=-3
\\\\
2-1-(-4)=-3
\\\\
2-1+4=-3
\\\\
5=-3
\text{ (FALSE)}
\\\\
\text{c. }\\
2x-y+z=-1
\\\\
2(2)-1+(-4)=-1
\\\\
4-1-4=-1
\\\\
-1=-1
\text{ (TRUE)}
\\\\
\text{d. }\\
-x-3y-z=-1
\\\\
-2-3(1)-(-4)=-1
\\\\
-2-3+4=-1
\\\\
-1=-1
\text{ (TRUE)}
.\end{array}
Hence, $\text{
equations a, c, d
}$ has the given point as solution.