Solve the System for X and Y Using Cramerʹs Rule $$\begin{array} { l } \frac { 1 } { a } x + \frac { 1 } { b } y = a b \\x + y = a\end{array}$$

question 285

Multiple Choice

Solve the system for x and y using Cramerʹs rule. Assume a and b are nonzero constants.
- $$\begin{array} { l } \frac { 1 } { a } x + \frac { 1 } { b } y = a b \\x + y = a\end{array}$$

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

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Definitions:

Subduction Zone

A region of the Earth's crust where two tectonic plates meet and one is forced below the other into the mantle, leading to volcanic activity and earthquakes.

Tilted Blocks

Geologic structures formed by the tilting of rock layers, often due to tectonic forces, creating an angle with the horizontal.

Anticlines

Upwardly convex folds in rock layers that typically have the oldest layers at their core.

Synclines

geological features formed by the downward folding of rock layers, with younger rocks in the core of the fold.