Question

plz answer it's urgent

Answer 1

$\frac{7x - 2y}{xy} = 5 \\ \\ \frac{7x}{xy} - \frac{2y}{xy} = 5 \\ \\ \frac{7}{y} - \frac{2}{x} = 5......(1) \\ \\ and \\ \\ \frac{8x + 7y}{xy} = 15 \\ \\ \frac{8x}{xy} + \frac{7y}{xy} = 15 \\ \\ \frac{8}{y} + \frac{7}{x} = 15.....(2) \\ \\ putting \: \frac{1}{y} = u \: and \: \frac{1}{x} = v \: in \: equation \: (1) \: and \: (2) \\ \\ 7u - 2v = 5....(3) \\ \\ and \\ \\ 8u + 7v = 15.....(4) \\ \\ from \: equation \: (3) \\ \\ 7u - 2v = 5 \\ \\ = > u = \frac{5 + 2v} {7} \\ \\ putting \: this \: value \: of \: u \: in \: equation \: (4) \\ \\ 8( \frac{5 + 2v}{7} ) + 7v = 15 \\ \\ = > 40 + 16v + 49v = 105 \\ \\ = > 65v = 105 - 40 \\ \\ = > 65v = 65 \\ \\ = > v = 1 \\ \\ putting \: this \: value \: of \: v \: in \: equation \: (3) \\ \\ 7u - 2 \times 1 = 5 \\ \\ = > 7u = 5 + 2 \\ \\ = > 7u = 7 \\ \\ = > u = 1 \\ \\ \\ therefore \: u = 1 \: and \: v = 1 \\ \\ \\ but \: u = \frac{1}{y} \\ \\ therefore \\ \\ x= \frac{1}{1} = 1 \\ \\ and \\ \\ v = \frac{1}{x} \\ \\ = > x = \frac{1}{v} = \frac{1}{1} = 1 \\ \\ \\ therefore \: x = 1 \: and \: y = 1$

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