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M + G = 37,    (1)
M - G =  5.    (2)
--------------------------Add the two equations.   You will get
M + M = 37 + 5,
2M = 42  ====>  M =  = 21.
Answer.  Maria is 21 years old.   George is 21-5 = 16 years old.
Check.   21 + 16 = 37    ! Correct !
 = 21.
Answer.  Maria is 21 years old.   George is 21-5 = 16 years old.
Check.   21 + 16 = 37    ! Correct !