Let $T\colon\mathbb{R}^2\to\mathbb{R}^2$ be given by $T(x,y) = (x + 2y, 3x + y)$.
I'm not sure if I plugged the values in the right place.
Ax. 1: $T(x + y) = T(x) + T(y)$
$[(x+2y) + 2(3x + y) + 3(x + 2y) - (3x - y)] = [(x+2y) + 2(3x + y)] + [3(x + 2y) - (3x - y)]$
Is that right?