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

---

Definitions:

Ectopic Pregnancy

A potentially life-threatening condition where a fertilized egg implants and grows outside the main cavity of the uterus, often in a fallopian tube.

Hydatidiform Mole

A rare growth that forms inside the womb at the beginning of a pregnancy, leading to an abnormal pregnancy.

Spontaneous Abortion

The natural ending of a pregnancy before the fetus can survive outside the womb, often referred to as a miscarriage.

Genital Herpes

A sexually transmitted infection (STI) caused by the herpes simplex virus (HSV) that results in genital sores and discomfort.