Solve the following pairs of linear equations:

$\dfrac{7x - 2y}{xy} = 5$

$\dfrac{8x + 7y}{xy} = 15$

Given,

$\dfrac{7x - 2y}{xy} = 5 \text{ or } \dfrac{7}{y} - \dfrac{2}{x} = 5$

$\dfrac{8x + 7y}{xy} = 15 \text{ or } \dfrac{8}{y} + \dfrac{7}{x} = 15$

Substituting $\dfrac{1}{x} = a \text{ and } \dfrac{1}{y} = b$ in above equations we get,

7b - 2a = 5 ……(i)

8b + 7a = 15 ……(ii)

Multiplying eq. (i) by 7 and eq. (ii) by 2 we get,

49b - 14a = 35 ……(iii)

16b + 14a = 30 …….(iv)

Adding equations (iii) and (iv) we get,

⇒ 49b - 14a + 16b + 14a = 35 + 30

⇒ 65b = 65

⇒ b = 1.

$\therefore \dfrac{1}{y} = 1 \\[1em] \Rightarrow y = 1.$

Substituting value of b in eq (i) we get,

⇒ 7(1) - 2a = 5

⇒ 7 - 2a = 5

⇒ 2a = 7 - 5

⇒ 2a = 2

⇒ a = 1.

$\therefore \dfrac{1}{x} = 1 \\[1em] \Rightarrow x = 1.$

Hence, x = 1 and y = 1.