L + S = 108,       (1)
L - 9 = 4*(S-9).   (2)

Express L via S from (1): L = 108 - S, and substitute it into (2).
You will get a single equation for S. 

108 - S - 9 = 4*(S-9).

Solve it:

108 -S - 9 = 4S - 36,

108 - 9 + 36 = 4S + S,

135 = 5S,

S =  = 27.

Shannon is 27 years old.

Now calculate Luis' age. It is 108 - S = 108 - 27 = 81.

Check. 27 + 81 = 108.  
       27 - 9 = 18.  81 - 9 = 72.   = 4.  OK.

Answer. Luis is 81 years old. Shannon age is 27 years.

Let Luis' age, be L

Then Shannon's is: 108 - L

We then get: L - 9 = 4(108 - L - 9)			

L - 9 = 4(99 - L)

L - 9 = 396 - 4L 

L + 4L = 396 + 9

5L = 405

L, or Luis' current age = , or  

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