let

e = Elliot's age

z = Zane's age

The sum of Elliot's age and twice Zane's age is 44

e + 2z = 44

The difference of twice Elliot's age and Zane's age is -2

e - z = -2

z = 2 + e plug into e + 2z = 44

e + 2(2 + e) = 44

3e + 4 = 44

e = 40/3

e = 13 1/3 years 13 years 12/3 months = 13 years 4 months

Elliot is 13 years 4 months old.