let

x = Alvin's age

y = Elga's age

Alvin is 13 years older than Elga:

x = y + 13

The sum of their ages is 97:

x + y = 97

by solving the system of equations:

x = y + 13

x + y = 97

we find:

x = 55 years

y = 42 years

click here to see the step by step solution of the system of equations:

Click to see all the steps

Elga's age is 42 years.