Question

use cramer's rule/ determinants to solve
8x-3y=5
2x+9y=-2

Answer 1

Are you solving for system of equation?

Answer 2

I can help you if you are.

Answer 3

Express the system using matrices:
\[\begin{bmatrix}8&-3\\2&9\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}\color{red}5\\\color{red}{-2}\end{bmatrix}\]
Cramer's rule can be used if the coefficient matrix has non-zero determinant:
\[\begin{vmatrix}8&-3\\2&9\end{vmatrix}=72-(-6)=78\not=0\]
Conditions are met, so we can use Cramer's to solve directly for \(x\) and \(y\):
\[x=\frac{\begin{vmatrix}\color{red}5&-3\\\color{red}{-2}&9\end{vmatrix}}{\begin{vmatrix}8&-3\\2&9\end{vmatrix}}~~\text{and}~~y=\frac{\begin{vmatrix}8&\color{red}5\\2&\color{red}{-2}\end{vmatrix}}{\begin{vmatrix}8&-3\\2&9\end{vmatrix}}\]