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

For this case we have the following system of equations:
 5x + 3y = 17
 -8x - 3y = 9
 We can rewrite the system like:
 Ax = b
 Where,
 A = [5   3; -8   -3]
 b = [17; 9]
 x = [x; y]
 The determinant of matrix A is given by:
 lAl = ((5) * (- 3)) - ((3) * (- 8))
 lAl = (-15) - (-24)
 lAl = -15 + 24
 lAl = 9
 
 The determinant for solving this linear system is:
 lAl = 9