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One solution
x + y = 14
x - y = 4
-----------------------Add the two equations. You will get
2x = 14 + 4 = 18 ====> x = 18/2 = 9.
Answer. 9 years and 14-9 = 5 years.
Another way
x + (x-4) = 14
2x - 4 = 14
2x = 14 + 4 = 18 ====> x = 18/2 = 9, and you get the same answer.