Answer
(a) The point $(x,y,z)=(-5,0,1)$ is not a solution of the system.
(b) The point $(x,y,z)=(10,0,-3)$ is a solution of the system.
Work Step by Step
The system of equations are
$\begin{cases} x+y+z=7\\ -2x+3y-2z=-14\\
-x-y+3z=-19\end{cases}$
(a) Let's substitute $(x,y,z)=(-5,0,1)$ in the first equation.
Then, we have $-5+0+1=7$ or $-4=7$ which is not true.
So, $(x,y,z)=(-5,0,1)$ is not a solution of the system.
(b) Substituting $(x,y,z)=(10,0,-3)$ in the system of equations, we get
$\begin{cases} 10+0+(-3)=7\\ -2(10)+3(0)-2(-3)=-14\\
-(10)-0+3(-3)=-19\end{cases}$
Simplifying, we have
$\begin{cases} 7=7\\ -14=-14\\
-19=-19\end{cases}$
Since all three equations are true, the point $(x,y,z)=(10,0,-3)$ is a solution of the system.