Use Cramer's Rule to solve (if possible) the system of equations. $\left\{ \begin{array} { r }
6 x - 5 y = 23 \
- 13 x + 3 y = - 89
\end{array} \right.$
A)(-8, -5)
B)(8, -5)
C)(-8, 5)
D)(8, 5)
E)(5, 8)

Question

Use Cramer's Rule to solve (if possible) the system of equations.   $\left\{ \begin{array} { r } 
6 x - 5 y = 23 \
- 13 x + 3 y = - 89
\end{array} \right.$  
A)(-8, -5)
B)(8, -5)
C)(-8, 5)
D)(8, 5)
E)(5, 8)

Quizplus · Accepted Answer

Cramer's Rule gives the solution as $x = \frac{D_x}{D}$ and $y = \frac{D_y}{D}$, where $D$ is the determinant of the coefficient matrix, and $D_x$ and $D_y$ are the determinants of the numerator matrices.$D = \begin{vmatrix} 6 & -5 \\ -13 & 3 \end{vmatrix} = (6)(3) - (-5)(-13) = 18 - 65 = -47$$D_x = \begin{vmatrix} 23 & -5 \\ -89 & 3 \end{vmatrix} = (23)(3) - (-5)(-89) = 69 + 445 = 514$$D_y = \begin{vmatrix} 6 & 23 \\ -13 & -89 \end{vmatrix} = (6)(-89) - (23)(-13) = -534 + 299 = -235$Therefore, $x = \frac{D_x}{D} = \frac{514}{-47} = -11$ and $y = \frac{D_y}{D} = \frac{-235}{-47} = 5$.The solution is $(-11, 5)$, which corresponds to choice D.

Use Cramer's Rule to Solve (If Possible) the System of Equations