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:

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Circumstances or events that can be anticipated or foreseen based on past experiences, patterns, or identifiable cues.

Uncertainty And Ambiguity

Conditions in which information is incomplete, unknown, or unclear, making decision-making and prediction challenging.

Respond Well

The ability to react positively and effectively to a situation or information.

Individual Resistance

Opposition or pushback by a person against changes or policies within an organization or group.