Solve the system for x and y using Cramer's rule. Assume a and b are nonzero constants.
-$$\begin{array} { l }
x + b y = a ^ { 2 } \
a x + y = b ^ { 2 }
\end{array}$$
A) $\left\{ \left( \frac { a ^ { 2 } - b ^ { 3 } } { a + b } , \frac { a ^ { 2 } - b ^ { 3 } } { a + b } \right) \right\}$
B) $\left\{ \left( - \frac { a ^ { 2 } - b ^ { 3 } } { a b } , - \frac { b ^ { 2 } - a ^ { 3 } } { a b } \right) \right\}$
C) $\left\{ \left( \frac { b ^ { 3 } } { 1 - a b } , \frac { a ^ { 3 } } { 1 - a b } \right) \right\}$
D) $\left\{ \left( \frac { a ^ { 2 } - b ^ { 3 } } { 1 - a b } , \frac { b ^ { 2 } - a ^ { 3 } } { 1 - a b } \right) \right\}$

Question

Solve the system for x and y using Cramer's rule. Assume a and b are nonzero constants.
-$$\begin{array} { l } 
x + b y = a ^ { 2 } \
a x + y = b ^ { 2 }
\end{array}$$
A) $\left\{ \left( \frac { a ^ { 2 } - b ^ { 3 } } { a + b } , \frac { a ^ { 2 } - b ^ { 3 } } { a + b } \right) \right\}$
B) $\left\{ \left( - \frac { a ^ { 2 } - b ^ { 3 } } { a b } , - \frac { b ^ { 2 } - a ^ { 3 } } { a b } \right) \right\}$
C) $\left\{ \left( \frac { b ^ { 3 } } { 1 - a b } , \frac { a ^ { 3 } } { 1 - a b } \right) \right\}$
D) $\left\{ \left( \frac { a ^ { 2 } - b ^ { 3 } } { 1 - a b } , \frac { b ^ { 2 } - a ^ { 3 } } { 1 - a b } \right) \right\}$

Quizplus · Accepted Answer

Cramer's rule involves calculating determinants. The determinant of the coefficient matrix and the determinants of matrices formed by replacing one column of the coefficient matrix with the constants on the right side of the equations are used to find the values of x and y. The correct solution, given the system of equations, is found by applying Cramer's rule correctly, leading to the answer in option D, where x and y are expressed in terms of a and b with the denominator $1 - ab$, which is the determinant of the coefficient matrix.

Solve the System for X and Y Using Cramer's Rule x+by=a2ax+y=b2\begin{array} { l } x + b y = a ^ { 2 } \\a x + y = b ^ { 2 }\end{array}x+by=a2ax+y=b2​

Solve the System for X and Y Using Cramer's Rule $\begin{array} { l } x + b y = a ^ { 2 } \\a x + y = b ^ { 2 }\end{array}$