Solve the system of linear equations. If the system has infinitely many solutions, describe the solution with an ordered triple in terms of variable z.
-$$\begin{array} { r r }
x + y + z & = 7 \
x - y + 2 z & = 7 \
2 x + 3 z & = 14
\end{array}$$
A) $\left( - \frac { 3 z } { 2 } - 7,2 z , z \right)$
B) $\left( - \frac { 3 z } { 2 } + 7 , \frac { z } { 2 } , z \right)$
C) $\left( - \frac { 3 z } { 2 } - 7 , \frac { z } { 2 } , z \right)$
D) $\left( - \frac { 3 z } { 2 } + 7,2 z , z \right)$

Question

Solve the system of linear equations. If the system has infinitely many solutions, describe the solution with an ordered triple in terms of variable z.
-$$\begin{array} { r r } 
x + y + z & = 7 \
x - y + 2 z & = 7 \
2 x + 3 z & = 14
\end{array}$$
A) $\left( - \frac { 3 z } { 2 } - 7,2 z , z \right)$
B) $\left( - \frac { 3 z } { 2 } + 7 , \frac { z } { 2 } , z \right)$
C) $\left( - \frac { 3 z } { 2 } - 7 , \frac { z } { 2 } , z \right)$
D) $\left( - \frac { 3 z } { 2 } + 7,2 z , z \right)$

Quizplus · Accepted Answer

The system of equations can be solved to express x and y in terms of z, resulting in the ordered triple $\left( - \frac { 3 z } { 2 } + 7 , \frac { z } { 2 } , z \right)$.

Solve the System of Linear Equations x+y+z=7x−y+2z=72x+3z=14\begin{array} { r r } x + y + z & = 7 \\x - y + 2 z & = 7 \\2 x + 3 z & = 14\end{array}x+y+zx−y+2z2x+3z​=7=7=14​

Solve the System of Linear Equations $\begin{array} { r r } x + y + z & = 7 \\x - y + 2 z & = 7 \\2 x + 3 z & = 14\end{array}$