Is the ordered triple a solution to the given system of equations?
-$$\begin{array} { l }
4 x + 2 y - 3 z = 7 \
2 x + 4 y + z = 35 \
6 x + 2 y - 2 z = 20
\end{array}$$
A) $\left( \frac { 7 } { 5 } , - \frac { 11 } { 3 } , 6 \right)$
B) $\left( - 7 , \frac { 11 } { 2 } , 6 \right)$
C) $\left( \frac { 7 } { 2 } , \frac { 11 } { 2 } , 6 \right)$
D) $\left( \frac { 11 } { 2 } , - \frac { 7 } { 2 } , - 6 \right)$

Question

Is the ordered triple a solution to the given system of equations?
-$$\begin{array} { l } 
4 x + 2 y - 3 z = 7 \
2 x + 4 y + z = 35 \
6 x + 2 y - 2 z = 20
\end{array}$$
A) $\left( \frac { 7 } { 5 } , - \frac { 11 } { 3 } , 6 \right)$
B) $\left( - 7 , \frac { 11 } { 2 } , 6 \right)$
C) $\left( \frac { 7 } { 2 } , \frac { 11 } { 2 } , 6 \right)$
D) $\left( \frac { 11 } { 2 } , - \frac { 7 } { 2 } , - 6 \right)$

Quizplus · Accepted Answer

Plug in the values of x, y, and z from option C into the system of equations:
$$\begin{array} { l } 
4 \left( \frac { 7 } { 2 } \right) + 2 \left( \frac { 11 } { 2 } \right) - 3(6) = 7 \
2 \left( \frac { 7 } { 2 } \right) + 4 \left( \frac { 11 } { 2 } \right) + 6 = 35 \
6 \left( \frac { 7 } { 2 } \right) + 2 \left( \frac { 11 } { 2 } \right) - 2(6) = 20
\end{array}$$
Simplifying each equation results in:
$$\begin{array} { l } 
7 = 7 \
35 = 35 \
20 = 20
\end{array}$$
Since all three equations are true, the ordered triple is indeed a solution to the system.

Is the Ordered Triple a Solution to the Given System 4x+2y−3z=72x+4y+z=356x+2y−2z=20\begin{array} { l } 4 x + 2 y - 3 z = 7 \\2 x + 4 y + z = 35 \\6 x + 2 y - 2 z = 20\end{array}4x+2y−3z=72x+4y+z=356x+2y−2z=20​

Is the Ordered Triple a Solution to the Given System $\begin{array} { l } 4 x + 2 y - 3 z = 7 \\2 x + 4 y + z = 35 \\6 x + 2 y - 2 z = 20\end{array}$