# Chapter 8 - Section 8.5 - Determinants and Cramer's Rule - Exercise Set - Page 945: 21

$(x,y)=(7,4)$

#### Work Step by Step

As per Cramer's Rule , we have $x=\dfrac{D_x}{D}$ and $y=\dfrac{D_y}{D}$ The general formula to calculate the determinant of a $2 \times 2$ matrix which has 2 rows and 2 columns, such as: $D=\begin{vmatrix}a&b\\c&d\end{vmatrix}=ad-bc$ Thus, $D=\begin{vmatrix}2&-3\\5&4\end{vmatrix}=23$ and $D_x=\begin{vmatrix}2&-3\\51&4\end{vmatrix}=161$ Also, $D_y=\begin{vmatrix}2&2\\5&51\end{vmatrix}=92$ Now, $x=\dfrac{D_x}{D}=7$ and $y=\dfrac{D_y}{D}=4$ Hence, $(x,y)=(7,4)$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.