2000019208

Let $[x,y,z]$ be the solution of the system $$\begin{array}{rlrl}x+2y& =\frac{7}{4}& & \\ y+3z& =2.5& & \\ 4x+z& =\frac{11}{3}& & \end{array}$$ What is the value of $x+y+z$?