Пояснення:

[tex]\displaystyle\\+\left \{ {{\frac{1}{x} +\frac{1}{y} =\frac{11}{30} } \atop {\frac{1}{x}-\frac{1}{y} =\frac{1}{30} }} \right. \ \ \ \ \ \ \Rightarrow\\\\\\\frac{1}{x} +\frac{1}{x} =\frac{11}{30}+\frac{1}{30} \\\\\\\frac{2}{x} =\frac{12}{30} =\frac{2}{5} \ |:2\\\\\\ \frac{1}{x} =\frac{1}{5} \ \ \ \ \ \ \Rightarrow\\\\x=5.\\\\\frac{1}{5} +\frac{1}{y} =\frac{11}{30} \\\\\\\frac{1}{y} =\frac{11}{30}-\frac{1}{5}=\frac{11-1*6}{30} =\frac{5}{30} =\frac{1}{6} .\ \ \ \ \ \ \Rightarrow\\\\y=6.[/tex]

Відповідь: (5;6).