[tex]\overline{2,1(a)}+\overline{2,a(1)}=\overline{a,1(2)}+\overline{1,a(2)}\\
2\frac{\overline{1a}-1}{90}+2\frac{\overline{a1}-a}{90}=a\frac{12-1}{90}+1\frac{\overline{a2}-a}{90}\\
\\
\frac{180+10+a-1}{90}+\frac{180+10a+1-a}{90}=\frac{90a+11}{90}+\frac{90+10a+2-a}{90} |\cdot 90\\
189+a+181+9a=90a+11+92+9a\\
370+10a=99a+103\\
267=89a\Rightarrow\boxed{a=3}\\[/tex]
