Determine if the given ordered triple is a solution of the system.
-$$\begin{array} { l }
( 4 , - 5,3 ) \
\left\{ \begin{array} { c }
x + y + z = 2 \
x - y + 2 z = 16 \
3 x + y + z = 8
\end{array} \right.
\end{array}$$
A) solution
B) not a solution

Question

Determine if the given ordered triple is a solution of the system.
-$$\begin{array} { l } 
( 4 , - 5,3 ) \
\left\{ \begin{array} { c } 
x + y + z = 2 \
x - y + 2 z = 16 \
3 x + y + z = 8
\end{array} \right.
\end{array}$$
A) solution
B) not a solution

Quizplus · Accepted Answer

Substituting $x = 4$, $y = -5$, and $z = 3$ into each equation of the system, we find that not all equations hold true. For example, in the first equation, $4 - 5 + 3 = 2$ is true, but in the second equation, $4 - (-5) + 2(3) = 4 + 5 + 6 = 15$, which does not equal 16. Therefore, the ordered triple is not a solution to the system.

Determine If the Given Ordered Triple Is a Solution of the System