If $(2,3)$ is a solution of the equation $7x - 3y = a$ and $(a, a+1)$ is a solution of the equation $2x + y = b$,find the values of $a$ and $b$.

(A) Step $1$: Substitute $(x, y) = (2, 3)$ into the equation $7x - 3y = a$.
$7(2) - 3(3) = a$
$14 - 9 = a$
$a = 5$.
Step $2$: Substitute $a = 5$ into the point $(a, a+1)$ to get $(5, 6)$.
Step $3$: Substitute $(x, y) = (5, 6)$ into the equation $2x + y = b$.
$2(5) + 6 = b$
$10 + 6 = b$
$b = 16$.
Thus,the values are $a = 5$ and $b = 16$.