Determine if the given ordered triple is a solution of the system.
-$$\begin{array} { r }
( 5,1,2 ) \
x + 2 y + 5 z = 17 \
2 y + 2 z = 6 \
z = 2
\end{array}$$
A) not a solution
B) solution

Question

Determine if the given ordered triple is a solution of the system.
-$$\begin{array} { r } 
( 5,1,2 ) \
x + 2 y + 5 z = 17 \
2 y + 2 z = 6 \
z = 2
\end{array}$$
A) not a solution
B) solution

Quizplus · Accepted Answer

To determine if the ordered triple (5,1,2) is a solution, we substitute x=5, y=1, and z=2 into each equation. For the first equation, 5 + 2(1) + 5(2) = 5 + 2 + 10 = 17, which matches the right side. For the second equation, 2(1) + 2(2) = 2 + 4 = 6, which also matches. The third equation is simply z = 2, which is true. Since all equations are satisfied, the ordered triple is a solution.

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