= Solution
For an <A2 root system> <weight> $w=(w_1,w_2)^T$, the specified <electric charge> and <flavour hypercharge> are the linear functionals
$$
q(w)=\frac{2w_1+w_2}{3},\qquad y(w)=\frac{w_1+2w_2}{3}.
$$
Apply these to the <meson octet> <weights> in <3/a/solution>. The results, with <electric charges> measured in units of the positive elementary <electric charge>, are
$$
\boxed{\begin{array}{c|rr|c}
w&q&y&\text{pseudoscalar octet member}\\\hline
(2,-1)&1&0&\pi^+\\
(-2,1)&-1&0&\pi^-\\
(1,1)&1&1&K^+\\
(-1,2)&0&1&K^0\\
(-1,-1)&-1&-1&K^-\\
(1,-2)&0&-1&\bar K^0\\
(0,0)\text{ twice}&0&0&\pi^0,\eta_8
\end{array}}
$$
The table illustrates the <meson octet> of <pseudoscalar mesons>; the same <weight> calculation applies to another <meson> species arranged in the same <representation>. Here <flavour hypercharge> is $Y=B+S$, with $B$ the <baryon number> and $S$ the <strangeness>, rather than <weak hypercharge>. If the full <quark model> <tensor product> $\mathbf3\otimes\overline{\mathbf3}$ is retained, its additional <trivial representation> is a ninth <meson> with $(q,y)=(0,0)$. This singlet is separate from the octet and need not share its <mass>.
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