Determine whether the system is inconsistent, dependent, or neither.
-$$\begin{array} { l }
x + y + z = - 5 \
x - y + 3 z = - 15 \
5 x + 5 y + 5 z = - 13
\end{array}$$
A)dependent
B)inconsistent
C)neither

Question

Determine whether the system is inconsistent, dependent, or neither.
-$$\begin{array} { l } 
x + y + z = - 5 \
x - y + 3 z = - 15 \
5 x + 5 y + 5 z = - 13
\end{array}$$
A)dependent
B)inconsistent
C)neither

Quizplus · Accepted Answer

The system is inconsistent because the third equation is a multiple of the first (multiplied by 5), but the right-hand side does not match (-25 vs. -13), indicating no solution exists that satisfies all three equations.

Determine Whether the System Is Inconsistent, Dependent, or Neither x+y+z=−5x−y+3z=−155x+5y+5z=−13\begin{array} { l } x + y + z = - 5 \\x - y + 3 z = - 15 \\5 x + 5 y + 5 z = - 13\end{array}x+y+z=−5x−y+3z=−155x+5y+5z=−13​

Determine Whether the System Is Inconsistent, Dependent, or Neither $\begin{array} { l } x + y + z = - 5 \\x - y + 3 z = - 15 \\5 x + 5 y + 5 z = - 13\end{array}$