I think you have a typo and you should have 12t in the first equation
If so, then drwls made the following observation
8s+12=16............. equation 1
6s+9t=12............. equation 2
Multiply equation 1 by 3 and equation 2 by 4 and subtract.
- - - (sign will change when sub)
put t=1 in equation 2
LHS=RHS so your answer is correct
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