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

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

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

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