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.
-$$\begin{aligned}
x + 8 y + 8 z & = 8 \
7 x + 7 y + z & = 1 \
8 x + 15 y + 9 z & = - 9
\end{aligned}$$
A) $\varnothing$
B) $\{ ( 0,0,1 ) \}$
C) $\{ ( 1 , - 1,1 ) \}$
D) $\{ ( - 1,0,1 ) \}$

Question

Quizplus · Accepted Answer

The system of equations is inconsistent, meaning there are no solutions that satisfy all three equations simultaneously. This can be determined through Gaussian elimination, which, when applied to this system, results in a contradiction indicating that no set of values for $x$, $y$, and $z$ can satisfy all equations.

Apply Gaussian Elimination to Systems Without Unique Solutions Use Gaussian x+8y+8z=87x+7y+z=18x+15y+9z=−9\begin{aligned}x + 8 y + 8 z & = 8 \\7 x + 7 y + z & = 1 \\8 x + 15 y + 9 z & = - 9\end{aligned}x+8y+8z7x+7y+z8x+15y+9z​=8=1=−9​

Apply Gaussian Elimination to Systems Without Unique Solutions
Use Gaussian $\begin{aligned}x + 8 y + 8 z & = 8 \\7 x + 7 y + z & = 1 \\8 x + 15 y + 9 z & = - 9\end{aligned}$