For this case we have the following system of equations:
[tex] 5x + 3y = 17
-8x - 3y = 9
[/tex]
We can Rewrite the system of equations of the form:
[tex] Ax = b
[/tex]
Where,
A: coefficient matrix
x: incognita vector
b: vector solution
We have then:
[tex] A=\left[\begin{array}{ccc}5&3\\-8&-3\end{array}\right] [/tex]
[tex] x=\left[\begin{array}{ccc}x\\y\end{array}\right] [/tex]
[tex] b=\left[\begin{array}{ccc}17\\9\end{array}\right] [/tex]
Then, the determinant of matrix A is given by:
[tex] |A|=(5)(-3)-(3)(-8)
[/tex]
[tex] |A|=-15+24 [/tex]
[tex] |A|=9 [/tex]
Answer:
The determinants for solving this linear system are:
[tex] |A|=9 [/tex]
