Apply Gaussian Elimination to Systems Without Unique Solutions
Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists.
-$$\begin{aligned}
x + y + z & = 9 \
2 x - 3 y + 4 z & = 7 \
x - 4 y + 3 z & = - 2
\end{aligned}$$
A) $\left\{ \left( - \frac { 7 z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } + \frac { 11 } { 5 } , z \right) \right\}$
B) $\left\{ \left( \frac { z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } + \frac { 11 } { 5 } , z \right) \right\}$
C) $\left\{ \left( - \frac { 7 z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } - \frac { 11 } { 5 } , z \right) \right\}$
D) $\left\{ \left( \frac { 7 z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } - \frac { 11 } { 5 } , z \right) \right\}$

Question

Quizplus · Accepted Answer

The correct solution set is obtained by applying Gaussian elimination to the system of equations, which results in a system with infinite solutions parameterized by $z$. The coefficients and constants in choice A correctly match the outcome of such a process, indicating a dependency on $z$ for the values of $x$ and $y$.

Apply Gaussian Elimination to Systems Without Unique Solutions Use Gaussian 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​

Apply Gaussian Elimination to Systems Without Unique Solutions
Use Gaussian $\begin{aligned}x + y + z & = 9 \\2 x - 3 y + 4 z & = 7 \\x - 4 y + 3 z & = - 2\end{aligned}$