Use Cramer's Rule to solve the following system of linear equations:

Question

Quizplus · Accepted Answer

We can write the system of linear equations in matrix form:

$\begin{bmatrix} 2 & -3 \ -1 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} -5 \ 2 \end{bmatrix}$

Then, we can use Cramer's Rule to solve for $x$ and $y$:

$x = \dfrac{\begin{vmatrix} -5 & -3 \ 2 & 4 \end{vmatrix}}{\begin{vmatrix} 2 & -3 \ -1 & 4 \end{vmatrix}} = \dfrac{14}{11}$

$y = \dfrac{\begin{vmatrix} 2 & -5 \ -1 & 2 \end{vmatrix}}{\begin{vmatrix} 2 & -3 \ -1 & 4 \end{vmatrix}} = \dfrac{-9}{11}$

Therefore, the solution to the system of linear equations is $(x,y) = (\frac{14}{11}, \frac{-9}{11})$. The correct choice is D.

Use Cramer's Rule to Solve the Following System of Linear