Determine if the given ordered triple is a solution of the system.
-$$\begin{array} { c }
( - 5 , - 1,4 ) \
x + y + z = - 2 \
x - y + 3 z = 8 \
5 x + y + z = - 22
\end{array}$$
A)solution
B)not a solution

Question

Determine if the given ordered triple is a solution of the system.
-$$\begin{array} { c } 
( - 5 , - 1,4 ) \
x + y + z = - 2 \
x - y + 3 z = 8 \
5 x + y + z = - 22
\end{array}$$
A)solution
B)not a solution

Quizplus · Accepted Answer

To determine if the ordered triple $(-5, -1, 4)$ is a solution, substitute $x = -5$, $y = -1$, and $z = 4$ into each equation and check if they hold true. For the first equation: $(-5) + (-1) + 4 = -2$, which is true. For the second equation: $(-5) - (-1) + 3(4) = -5 + 1 + 12 = 8$, which is also true. For the third equation: $5(-5) + (-1) + 4 = -25 - 1 + 4 = -22$, which is true as well. Since the ordered triple satisfies all three equations, it is indeed a solution to the system.

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