Determine if the given ordered triple is a solution of the system.
-$$\begin{array} { l }
( 1 , - 3,3 ) \
2 x + 4 y + z = - 5 \
4 x - 3 y - z = 20 \
4 x + y + 3 z = 12
\end{array}$$
A) not a solution
B) solution

Question

Determine if the given ordered triple is a solution of the system.
-$$\begin{array} { l } 
( 1 , - 3,3 ) \
2 x + 4 y + z = - 5 \
4 x - 3 y - z = 20 \
4 x + y + 3 z = 12
\end{array}$$
A) not a solution
B) solution

Quizplus · Accepted Answer

Substituting the values from the ordered triple (1,-3,3) into the system of equations, we get:
\begin{align*}
2x+4y+z &= 2(-3)+4(1)+3 = -6+4+3 = 1 
eq -5 \
4x-3y-z &= 4(1)-3(-3)-3 = 4+9-3 = 10 
eq 20 \
4x+y+3z &= 4(1)+(-3)+3(3) = 4-3+9 = 10 
eq 12
\end{align*}
Since at least one of the equations does not hold true when we plug in the values of the ordered triple, it is not a solution to the system. Therefore, the best choice is A, not a solution.

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