Solve the System for X and Y Using Cramerʹs Rule $$\begin{array} { l } x + b y = a ^ { 2 } \\a x + y = b ^ { 2 }\end{array}$$

question 339

Multiple Choice

Solve the system for x and y using Cramerʹs rule. Assume a and b are nonzero constants.
- $$\begin{array} { l } x + b y = a ^ { 2 } \\a x + y = b ^ { 2 }\end{array}$$

• A) \(\left\{ \left( \frac { a ^ { 2 } - b ^ { 3 } } { a + b } , \frac { a ^ { 2 } - b ^ { 3 } } { a + b } \right) \right\}\)
• B) \(\left\{ \left( \frac { a ^ { 2 } - b ^ { 3 } } { 1 - a b } , \frac { b ^ { 2 } - a ^ { 3 } } { 1 - a b } \right) \right\}\)
• C) \(\left\{ \left( - \frac { a ^ { 2 } - b ^ { 3 } } { a b } , - \frac { b ^ { 2 } - a ^ { 3 } } { a b } \right) \right\}\)
• D) \(\left\{ \left( \frac { b ^ { 3 } } { 1 - a b } , \frac { a ^ { 3 } } { 1 - a b } \right) \right\}\)

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Definitions:

Error of Estimation

Error of estimation is the discrepancy between an estimated value and the true value of a parameter being estimated.

Sampling Error

The error caused by observing a sample instead of the whole population, affecting the precision of statistical estimates.

Population Standard Deviation

The square root of the variance in a population, reflecting how much individual data points in the entire population deviate from the population mean.

Confidence Level

The degree of certainty or probability with which a parameter of a population is estimated.