Solve the following simultaneous equations: (7x - 2y)/(xy) = 5 ; (8x + 7y)/(xy) = 15

Answer: \((x, y) = (1, 1)\)

Split the fractions: \(\frac{7x}{xy} - \frac{2y}{xy} = \frac{7}{y} - \frac{2}{x} = 5\) and \(\frac{8}{y} + \frac{7}{x} = 15\).

Put \(\frac{1}{x} = m\), \(\frac{1}{y} = n\): \(-2m + 7n = 5\) ... (I), \(7m + 8n = 15\) ... (II).

Multiply (I) by 7 and (II) by 2: \(-14m + 49n = 35\), \(14m + 16n = 30\). Adding: \(65n = 65\), \(n = 1\).

From (I): \(-2m = 5 - 7 = -2\), \(m = 1\). So \(x = 1\), \(y = 1\).