Find All Solutions of the System $$\left\{ \begin{array} { r } x + y + z = 12 \\2 x - y - z = - 5 \\6 x + 2 y + z = 30\end{array} \right.$$

question 4

Multiple Choice

Find all solutions of the system. $$\left\{ \begin{array} { r } x + y + z = 12 \\2 x - y - z = - 5 \\6 x + 2 y + z = 30\end{array} \right.$$

• A) \(\left( \frac { 10 } { 3 } , \frac { 16 } { 3 } , \frac { 10 } { 3 } \right)\)
• B) \(\left( 19 , \frac { 10 } { 3 } , \frac { 7 } { 3 } \right)\)
• C) \(\left( \frac { 7 } { 3 } , \frac { 19 } { 3 } , \frac { 10 } { 3 } \right)\)
• D) \(\text { The system is dependent. }\)
• E) \(\text { The system is inconsistent. }\)

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Definitions:

Periodic Inventory System

An inventory accounting system where updates to inventory accounts occur at specific intervals, typically at the end of an accounting period.

LIFO

An inventory valuation method where the last items added to inventory are considered the first ones sold during a period of time; stands for Last-In, First-Out.

FIFO

An accounting method for inventory valuation where the first items acquired are the first ones sold, standing for First In, First Out.

Inventory Turnover

A ratio showing how many times a company's inventory is sold and replaced over a specific period, indicating the efficiency in managing stock levels.