System

The answer is

\(s=-\frac{62}{23}\\ t=-\frac{33}{23}\)

First , simplify the equations :

s/2   + 5t = 3 - 7t + 8s 

   =    S + 10T = 6 - 14T + 16S

     =  24T = 15S + 6 

3T - 6S = 9 - 2T

= 5T = 6S + 9         Multiply this equation by -2.5 to get 

  -12.5 t = -15s - 22.5      And add this to the first equation

   11.5 t =  - 16.5

        T = - 16.5/11.5  = - 33/23       Use this value in one of the equations to solve for s :      S =  - 62/23