Determine whether the ordered triple is a solution of the system of equations. $\left\{ \begin{array} { l }
3 x + 4 y - z = 16 \
5 x - y + 2 z = 26 \
2 x - 3 y + 7 z = 30
\end{array} \right.$
$( 4,2,4 )$

Question

Determine whether the ordered triple is a solution of the system of equations.  $\left\{ \begin{array} { l } 
3 x + 4 y - z = 16 \
5 x - y + 2 z = 26 \
2 x - 3 y + 7 z = 30
\end{array} \right.$ 
$( 4,2,4 )$

Quizplus · Accepted Answer

Substituting $x = 4$, $y = 2$, and $z = 4$ into each equation: For the first equation, $3(4) + 4(2) - 4 = 12 + 8 - 4 = 16$. For the second equation, $5(4) - 2 + 2(4) = 20 - 2 + 8 = 26$. For the third equation, $2(4) - 3(2) + 7(4) = 8 - 6 + 28 = 30$. Since all equations are satisfied, the ordered triple $(4,2,4)$ is indeed a solution to the system of equations.

Determine Whether the Ordered Triple Is a Solution of the System