For this case we have the following system of equations:

We can Rewrite the system of equations of the form:

Where,
A: coefficient matrix
x: incognita vector
b: vector solution
We have then:
![A=\left[\begin{array}{ccc}5&3\\-8&-3\end{array}\right]](https://img.qammunity.org/2019/formulas/mathematics/high-school/3oxh74y09djv6k8f678w8w8kspruxgiof2.png)
![x=\left[\begin{array}{ccc}x\\y\end{array}\right]](https://img.qammunity.org/2019/formulas/mathematics/high-school/zww611arw4lh6evxmugs3auv56tge1xtnx.png)
![b=\left[\begin{array}{ccc}17\\9\end{array}\right]](https://img.qammunity.org/2019/formulas/mathematics/high-school/mlxfh1pf36v712pn1xgno7y1y4wivckmys.png)
Then, the determinant of matrix A is given by:



Answer:
The determinants for solving this linear system are:
