In this problem, $a$ and $b$ are integers, such that $a \ge b.$ If $a+b\equiv 2\pmod{10}$ and $2a+b\equiv 1\pmod{10}$, then what is the last digit of $a-b$?

(2a + b) - (a + b) = 1 - 2 (mod 10)

a = 9 (mod 10)

a + b = 2 (mod 10)

9 + b = 2 (mod 10)

b = 3

a = 9, b = 3, a - b = 6

=^._.^=