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

question 470

Multiple Choice

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

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

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Definitions:

Organic Letters

A peer-reviewed scientific journal publishing original research articles in organic chemistry.

Molecular Orbitals

Orbitals that belong to a molecule as a whole, where electrons are considered to be delocalized over the entire molecule.

Electrophile

A chemical species that accepts an electron pair from a nucleophile to form a chemical bond.

Major Organic Product

The primary compound resulting from an organic reaction, often highlighting the significance of reactant structure and conditions used.