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:

Opportunity Cost

The lost potential gain from other alternatives when one alternative is chosen.

Income Effects

The changes in an individual's or economy's income and how that changes their spending and saving behavior.

Substitution Effects

The change in consumption patterns due to a change in the relative prices of goods.

Normal Goods

Goods for which demand goes up when income is higher and for which demand goes down when income is lower.