Determine if the given ordered triple is a solution of the system.
-$$\begin{array} { l }
( - 3 , - 1,5 ) \
5 x + 4 y + z = - 14 \
2 x - 2 y - z = - 9 \
3 x + y + 5 z = 15
\end{array}$$
A) solution
B) not a solution

Question

Determine if the given ordered triple is a solution of the system.
-$$\begin{array} { l } 
( - 3 , - 1,5 ) \
5 x + 4 y + z = - 14 \
2 x - 2 y - z = - 9 \
3 x + y + 5 z = 15
\end{array}$$
A) solution
B) not a solution

Quizplus · Accepted Answer

To determine if the ordered triple $(-3, -1, 5)$ is a solution, substitute $x = -3$, $y = -1$, and $z = 5$ into each equation and check if they hold true. For the first equation, $5(-3) + 4(-1) + 5 = -15 - 4 + 5 = -14$, which is true. For the second equation, $2(-3) - 2(-1) - 5 = -6 + 2 - 5 = -9$, which is also true. For the third equation, $3(-3) + (-1) + 5(5) = -9 - 1 + 25 = 15$, which is true as well. Since the ordered triple satisfies all three equations, it is a solution to the system.

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