Solve the System for X and Y Using Cramer's Rule $$\frac { 1 } { a } x + \frac { 1 } { b } y = a b$$

question 499

Multiple Choice

Solve the system for x and y using Cramer's rule. Assume a and b are nonzero constants.
- $$\frac { 1 } { a } x + \frac { 1 } { b } y = a b$$
$x + y = a$

• A) \(\left\{ \left\{ \frac { a ( b - a ) \left( b ^ { 2 } - 1 \right) } { a b ^ { 2 } } , \frac { ( b - a ) ( 1 - a b ) } { a b } \right) \right\}\)
• B) \(\left\{ \left\{ \frac { a ^ { 2 } b \left( b ^ { 2 } - 1 \right) } { b - a } , \frac { a b ( 1 - a b ) } { b - a } \right) \right\}\)
• C) \(\left\{ \left( \frac { a ^ { 2 } \left( b ^ { 2 } - 1 \right) } { b - a } , \frac { a b ( 1 - a b ) } { b - a } \right] \right\}\)
• D) \(\left\{ \left( a b ( 1 - a b ) , a ^ { 2 } \left( b ^ { 2 } - 1 \right) \right) \right\}\)

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Definitions:

Marginal Utility

The extra gratification or advantage a person receives by consuming an additional unit of a specific good or service.

Marginal Utilities

The extra pleasure or benefit a consumer gets from purchasing and using an additional unit of a product or service.

Utility-Maximizing

A principle in economics where consumers aim to achieve the highest level of satisfaction with their choices, subject to their income and the prices of goods and services.

Marginal Utility

Marginal Utility represents the additional satisfaction or utility a consumer gains from consuming one more unit of a good or service.