my homework do it

Prove by induction that each positive integer n ≥ 8 can be represented in the form
n = 3a + 5b, where a and b are non-negative integers.

3a + 5b = 3a + 3b + 2b
= 3(a+b) + 2b, with a and b an element of N
= 3c + 2(c-a), with a and c an element of N
= 3c + 2c - 2a
= 5c - 2a = 1 for c = 1 and a = 2 -> you can make steps of 1 from n = 3*1 + 5*1 = 8

QED