Ages of two friends

Let a be the age of the older person and b be the age of the younger person.

The first equation is: a + b = 30 and the second equation is: a – b = 10.

Solving the system of equations gives a = 20 and b = 10. So the younger person is 10 years old.

\[\begin{cases} x+y = 30 &\ldots (1) \\ x-y = 10 &\ldots (2) \end{cases}

\quad \quad \quad \quad (1) + (2)\implies 2x = 40 \implies \boxed{x = 20, y = 10}\]