Maths ( Higher Level) Simultaneous Equations.

A mother is x years old, her son is y years old and the sum of theirs ages together is 58 years. Five years ago, the mother was five times as old as the son. Write two equations in x and y and solve them to find the age of their mother and age of the son.

I have found out the answer, but the problem is that I do not know the METHOD of finding the answer.
Please reply asap if you are able. Thank You.

Answers:

Mother = 45
Son = 13

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  1. the method is just to write the words as math:

    mother is x years old, her son is y years old and the sum of theirs ages together is 58

    x+y = 58

    Five years ago, the mother was five times as old as the son

    (x-5) = 5(y-5)

    Now it's easy!

    x+y=58
    x-5y = -20

    subtract and you get

    6y = 78
    y = 13
    so, x=58-y = 45

    5 years ago they were 40 and 8; 40=5*8

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