Determine if the given ordered triple is a solution of the system.
-$$\begin{array} { l }
( - 4 , - 1,5 ) \
2 x + 2 y + z = - 5 \
5 x - 4 y - z = - 21 \
5 x + y + 2 z = - 11
\end{array}$$
A) solution
B) not a solution

Question

Determine if the given ordered triple is a solution of the system.
-$$\begin{array} { l } 
( - 4 , - 1,5 ) \
2 x + 2 y + z = - 5 \
5 x - 4 y - z = - 21 \
5 x + y + 2 z = - 11
\end{array}$$
A) solution
B) not a solution

Quizplus · Accepted Answer

To determine if the ordered triple $(-4, -1, 5)$ is a solution, substitute $x = -4$, $y = -1$, and $z = 5$ into each equation and check if they hold true. For the first equation: $2(-4) + 2(-1) + 5 = -8 - 2 + 5 = -5$, which matches. For the second equation: $5(-4) - 4(-1) - 5 = -20 + 4 - 5 = -21$, which also matches. For the third equation: $5(-4) + (-1) + 2(5) = -20 - 1 + 10 = -11$, which matches as well. Since all three equations are satisfied, the ordered triple is indeed a solution to the system.

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