Solve the System in Terms of the Arbitrary Variable X $$\begin{array} { r } x + y + z = 9 \\4 x - 3 y + 2 z = 7\end{array}$$

question 269

Multiple Choice

Solve the system in terms of the arbitrary variable x.
- $$\begin{array} { r } x + y + z = 9 \\4 x - 3 y + 2 z = 7\end{array}$$

• A) \(\left\{ \left( x , \frac { 2 x + 11 } { 5 } , \frac { - 7 x + 34 } { 5 } \right) \right\}\)
• B) \(\left\{ \left( x , \frac { 2 x - 11 } { 5 } , \frac { - 7 x + 34 } { 5 } \right) \right\}\)
• C) \(\left\{ \left\{ x , \frac { 2 x + 11 } { 5 } , \frac { x + 34 } { 5 } \right) \right\}\)
• D) \(\varnothing\)

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Definitions:

Rational Consumer

An economic concept assuming that consumers make decisions to maximize their utility based on available information and their preferences.

Consumer Equilibrium

In marginal utility theory, the combination of goods purchased that maximizes total utility by applying the utility-maximizing rule. In indifference curve analysis, the combination of goods purchased that maximizes total utility by enabling the consumer to reach the highest indifference curve, given the consumer’s budget line (or budget constraint).

Prices

The amount of money required to purchase goods or services, often determined by supply and demand dynamics.

Utility-maximizing Combination

This refers to a situation where a consumer selects a combination of goods and services that provides the highest level of satisfaction or utility, given their budget constraint.