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.
-$$\begin{aligned}
x + y + z & = 9 \
2 x - 3 y + 4 z & = 7 \
x - 4 y + 3 z & = - 2
\end{aligned}$$
A) $\left( \frac { z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } + \frac { 11 } { 5 } , z \right)$
B) $\left( - \frac { 7 z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } + \frac { 11 } { 5 } , z \right)$
C) $\left( \frac { 7 z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } - \frac { 11 } { 5 } , z \right)$
D) $\left( - \frac { 7 z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } - \frac { 11 } { 5 } , z \right)$

Question

Quizplus · Accepted Answer

The system of equations is consistent and dependent, leading to infinitely many solutions. Solving the system using substitution or elimination gives the solution in terms of z as $\left( - \frac { 7 z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } + \frac { 11 } { 5 } , z \right)$.

Solve the System of Linear Equations x+y+z=92x−3y+4z=7x−4y+3z=−2\begin{aligned}x + y + z & = 9 \\2 x - 3 y + 4 z & = 7 \\x - 4 y + 3 z & = - 2\end{aligned}x+y+z2x−3y+4zx−4y+3z​=9=7=−2​

Solve the System of Linear Equations $\begin{aligned}x + y + z & = 9 \\2 x - 3 y + 4 z & = 7 \\x - 4 y + 3 z & = - 2\end{aligned}$