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

Question

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

Quizplus · Accepted Answer

Substituting the values of $x$, $y$, and $z$ from the ordered triple $(-3, 2, 3)$ into both equations, we find that the first equation $x + y + z = 2$ becomes $(-3) + 2 + 3 = 2$, which is true. However, the second equation $x - y + 2z = -5$ becomes $(-3) - 2 + 2(3) = -3$, which is not equal to $-5$. Therefore, the ordered triple does not satisfy both equations simultaneously, making it not a solution to the system.

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