Answer
a. The point $(x,y,z)=(1,-2,4)$ is not the solution of the system.
a. The point $(x,y,z)=(0,0,4)$ is not the solution of the system.
Work Step by Step
The given system is
$\left\{\begin{matrix}
-x &+y &+z& = &1 \\
x& +2y & -z&= &-7 \\
3x&-y&+z&=&9
\end{matrix}\right.$
a.
Substitute $(x,y,z)=(1,-2,4)$ into all three equations.
$\left\{\begin{matrix}
-1 &-2 &+4& = &1 \\
1& +2(-2) & -4&= &-7 \\
3(1)&-(-2)&+4&=&9
\end{matrix}\right.$
Simplify.
$\left\{\begin{matrix}
1 & = &1 \\
-7&= &-7 \\
11&=&9
\end{matrix}\right.$
The last equation is not true, the point $(x,y,z)=(1,-2,4)$ is not a solution of the system.
b.
Substitute $(x,y,z)=(0,0,4)$ into all three equations.
$\left\{\begin{matrix}
-0 &+0 &+4& = &1 \\
0& +2(0) & -4&= &-7 \\
3(0)&-(0)&+4&=&9
\end{matrix}\right.$
Simplify.
$\left\{\begin{matrix}
4& = &1 \\
-4&= &-7 \\
4&=&9
\end{matrix}\right.$
All three equations are not true, the point $(x,y,z)=(0,0,4)$ is not a solution of the system.
