Solve the system for x and y using Cramerʹs 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) $\left\{ \left( \frac { a ^ { 2 } - b ^ { 3 } } { 1 - a b } , \frac { b ^ { 2 } - a ^ { 3 } } { 1 - a b } \right) \right\}$
C) $\left\{ \left( - \frac { a ^ { 2 } - b ^ { 3 } } { a b } , - \frac { b ^ { 2 } - a ^ { 3 } } { a b } \right) \right\}$
D) $\left\{ \left( \frac { b ^ { 3 } } { 1 - a b } , \frac { a ^ { 3 } } { 1 - a b } \right) \right\}$

Question

Solve the system for x and y using Cramerʹs 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) $\left\{ \left( \frac { a ^ { 2 } - b ^ { 3 } } { 1 - a b } , \frac { b ^ { 2 } - a ^ { 3 } } { 1 - a b } \right) \right\}$
C) $\left\{ \left( - \frac { a ^ { 2 } - b ^ { 3 } } { a b } , - \frac { b ^ { 2 } - a ^ { 3 } } { a b } \right) \right\}$
D) $\left\{ \left( \frac { b ^ { 3 } } { 1 - a b } , \frac { a ^ { 3 } } { 1 - a b } \right) \right\}$

Quizplus · Accepted Answer

Cramer's rule uses determinants to solve a system of linear equations. For the given system, the determinant (D) of the coefficient matrix and the determinants $D_x$ and $D_y$ for the matrices with the columns replaced by the constants on the right side of the equations are calculated. The solutions are $x = D_x / D$ and $y = D_y / D$. The correct solution is found by calculating these determinants, leading to the answer in choice B, which correctly applies Cramer's rule to the given system.

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