解:由题意,得$\sqrt {x - 2y + 9}+(x - y - 3)^2 = 0$
∵$\sqrt {x - 2y + 9}\geq 0,$$(x - y - 3)^2\geq 0$
∴$x - 2y + 9 = 0,$$x - y - 3 = 0$
联立方程组$\begin {cases}x - 2y + 9 = 0 \\x - y - 3 = 0 \end {cases},$解得$\begin {cases}{x=15}\\{y = 12}\end {cases}$
∴$2x-\frac 13y = 2×15-\frac 13×12 = 30 - 4 = 26$
则$2x-\frac 13y$的算术平方根为$\sqrt {26}$