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

question 155

Multiple Choice

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

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

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Definitions:

Standard Error

A statistical measure that describes the accuracy with which a sample represents a population, specifically the variability of the sampling distribution.

Sample Mean

The average of a set of numerical values taken from a subset (sample) of a larger population.

Probability

A measure of the likelihood of a particular event's occurrence, ranging from 0 (impossible) to 1 (certain).

P < 0.05

Indicates that the probability of the observed data, or more extreme, occurring by chance is less than 5%, commonly used to determine statistical significance in hypothesis testing.