If the system of linear equations :
$$x + y + 2z = 6$$
$$2x + 3y + \mathrm { a } z = \mathrm { a } + 1$$
$$- x - 3 y + \mathrm { b } z = 2 \mathrm {~b}$$
where $a , b \in \mathbf { R }$, has infinitely many solutions, then $7a + 3b$ is equal to :\\
(1) 16\\
(2) 12\\
(3) 22\\
(4) 9