Solve the matrix equation $Mz = a + b$ for $z$ where $M = \left[ \begin{array} { l l } { 1 } & { 1 } \\ { 3 } & { 4 } \end{array} \right]$, $a = \left[ \begin{array} { l } { 4 } \\ { 3 } \end{array} \right]$, and $b = \left[ \begin{array} { l } { 2 } \\ { 2 } \end{array} \right]$.