Find the Solution or Solutions, If Any Exist, to the System

question 67

Multiple Choice

Find the solution or solutions, if any exist, to the system.
- $$\left\{ \begin{array} { c } x + 4 y - 2 z = - 5 \\3 x - 6 y + 6 z = 7 \\5 x + 2 y + 2 z = - 3\end{array} \right.$$

• A) infinitely many solutions of the form \(x = - \frac { 1 } { 9 } - \left( \frac { 2 } { 3 } \right) z , y = - \frac { 11 } { 9 } + \left( \frac { 2 } { 3 } \right) z , z = z\)
• B) \(x = 0 , y = 0 , z = 1\)
• C) infinitely many solutions of the form \(x = 8 - \frac { 2 } { 9 } z , y = 1 - \frac { 17 } { 18 } z , z = z\)
• D) inconsistent system, no solution

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Definitions:

Algebra Problem

A mathematical question or exercise that requires the application of algebraic methods and principles for its solution.

Controlled Processes

Mental activities requiring focused attention and generally interfering with other ongoing activities.

Selective Attention

The act of focusing on a specific aspect of experience while ignoring others.

REM Sleep

A stage of sleep characterized by rapid eye movement when most vivid dreams occur.