Determine if the given ordered triple is a solution of the system.
-$$\left\{ \begin{array} { c }
( 0 , - 4 , - 3 ) \
3 x - y + 5 z = - 11 \
x + z = - 3 \
x + 2 y + z = - 11
\end{array} \right.$$
A) not a solution
B) solution

Question

Determine if the given ordered triple is a solution of the system.
-$$\left\{ \begin{array} { c } 
( 0 , - 4 , - 3 ) \
3 x - y + 5 z = - 11 \
x + z = - 3 \
x + 2 y + z = - 11
\end{array} \right.$$
A) not a solution
B) solution

Quizplus · Accepted Answer

To verify if the ordered triple $(0, -4, -3)$ is a solution, we substitute $x = 0$, $y = -4$, and $z = -3$ into each equation of the system. For the first equation, $3(0) - (-4) + 5(-3) = 0 + 4 - 15 = -11$, which matches the right side of the equation. For the second equation, $0 + (-3) = -3$, which is true. For the third equation, $0 + 2(-4) + (-3) = -8 - 3 = -11$, which also matches the right side of the equation. 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