Determine whether the given ordered triple is a solution of given system. $( 5,1,1 ) , \left\{ \begin{array} { l }
x - y + z = 5 \
2 x + y - z = 10 \
2 x - 3 y + z = 8
\end{array} \right.$

Question

Determine whether the given ordered triple is a solution of given system. $( 5,1,1 ) , \left\{ \begin{array} { l } 
x - y + z = 5 \
2 x + y - z = 10 \
2 x - 3 y + z = 8
\end{array} \right.$

Quizplus · Accepted Answer

To check if the ordered triple (5,1,1) is a solution to the given system, we substitute the values of x, y, and z in each equation and see if the equations hold true.

Substituting (5,1,1) in the first equation, we get:
5 - 1 + 1 = 5, which is true.

Substituting (5,1,1) in the second equation, we get:
2(5) + 1 - 1 = 10, which is true.

Substituting (5,1,1) in the third equation, we get:
2(5) - 3(1) + 1 = 8, which is true.

Therefore, (5,1,1) is a solution to the given system, and the answer is A.

Determine Whether the Given Ordered Triple Is a Solution of Given