What are the determinants for solving this linear system? 5x + 3y = 17 −8x − 3y = 9 |A| = |Ax| = |Ay| =

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]