Find the value of a and b so that the pair of values (2, -3) is a solution of the system
x + by = 5
ax -3y = -1

X = 2 y =-3 Plug these values in;-

2 - 3b = 5
2a + 9 = -1

from first equation -3b = 3  so b = -1
from second equation 
2a = -10 so a = -5

Since (2, -3) is a solution, that means x = 2 and y = -3 would satisfy the equations.

x + by = 5                                              Ax - 3y = -1

2 + b*-3 = 5                                          A*2 - 3*-3 = -1

2 - 3b =5                                              2A + 9 = -1

-3b = 5 - 2                                            2A = -1 - 9  

-3b = 3                                                  2A = -10

b = 3/-3                                                    A = -10/2 

b = -1                                                        A = -5

b = -1 and A = -5

Hope this helps.