Solve :

$\dfrac{3}{x} + \dfrac{2}{y} = 10$

$\dfrac{9}{x} - \dfrac{7}{y} = 10.5$

Given, equations :

$\Rightarrow \dfrac{3}{x} + \dfrac{2}{y} = 10$ …………(1)

$\Rightarrow \dfrac{9}{x} - \dfrac{7}{y} = 10.5$ ……….(2)

Multiplying equation (1) by 3, we get :

$\Rightarrow 3\Big(\dfrac{3}{x} + \dfrac{2}{y}\Big) = 3 \times 10 \\[1em] \Rightarrow \dfrac{9}{x} + \dfrac{6}{y} = 30 ……….(3)$

Subtracting equation (2) from (3), we get :

$\Rightarrow \Big(\dfrac{9}{x} + \dfrac{6}{y}\Big) - \Big(\dfrac{9}{x} - \dfrac{7}{y}\Big) = 30 - 10.5 \\[1em] \Rightarrow \dfrac{9}{x} - \dfrac{9}{x} + \dfrac{6}{y} + \dfrac{7}{y} = 19.5 \\[1em] \Rightarrow \dfrac{13}{y} = 19.5 \\[1em] \Rightarrow y = \dfrac{13}{19.5} \\[1em] \Rightarrow y = \dfrac{1}{1.5} = \dfrac{2}{3}.$

Substituting value of y in equation (1), we get :

$\Rightarrow \dfrac{3}{x} + \dfrac{2}{\dfrac{2}{3}} = 10 \\[1em] \Rightarrow \dfrac{3}{x} + \dfrac{6}{2} = 10 \\[1em] \Rightarrow \dfrac{3}{x} + 3 = 10 \\[1em] \Rightarrow \dfrac{3}{x} = 7 \\[1em] \Rightarrow x = \dfrac{3}{7}.$

Hence, x = $\dfrac{3}{7} \text{ and } y = \dfrac{2}{3}$.