Question

7x-2y/xy =5;8x+7y/xy=15 simultaneous equation

Answer 1

$\frac{7x - 2y}{xy} = 5 \: \: \: \: = > \frac{7}{y} - \frac{2}{x} = 5 \\ \frac{8x + 7y}{xy} = 15 \: = > \frac{8}{y} + \frac{7}{x} = 15 \\ let \: \: \frac{1}{y} = p \ \: \: and \: \: \: \frac{1}{x} = q \: \: \: \: \: \: \: we \: get \: \\ 7p - 2q = 5 \: \: \: \: \: \: .........(1) \\ 8p + 7q = 15 \: \: \: \: .........(2) \\ multiply \: equation \: (1) \: with \: 8 \: and \: eqation \: (2) \: with \: 7 \: \: \: \: \: we \: get \\ 56p - 16q = 40 \: \: \: \: \: .....(3)\\ 56p + 49q = 105 \: \: \: \: \: \: ....(4) \\ subtract \: equation \: (4) \: from \: equation \: (3) \: \: we \: get \\ - 65q = - 65 \\ q = 1 \\ substitute \: the \: value \: of \: q = 1 \: in \: equation \: (1) \\ 7p - 2(1) = 5 \\ 7p = 5 + 2 \\ 7p = 7 \\ p = 1 \: \\ \frac{1}{y } = p \\ \frac{1}{y} = 1 \\ y = 1 \\ and \\ \frac{1}{x} = q \\ \frac{1}{x} = 1 \\ x= 1$