Question

21 X + 47 y equal to 110 47 X + 21 Y equal to 162
$\frac{21}{x} + \frac{47}{y} = 110 \: and \: \frac{47}{x} + \frac{21}{y} = 162$
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Answer 1

Answer:

$x = 1 \\ y = \frac{1}{3}$

Step-by-step explanation:

Given:-

$\frac{21}{x} + \frac{47}{y} = 110 \\ \\ \frac{47}{x} + \frac{21}{y} = 162 \\ \\ now \\ \\ assume \: that \: \frac{1}{x} = a \: \: \\ and \: \frac{1}{y} = b \\ \\ there \: for \\ \\ 21a + 47b = 110 \: \: \: ...........(1) \\ \\ 47a + 21b = 162 \: \: \: ..............(2) \\ \\ now \: add \: equation \: 1 \: and \: 2 \\ \\ \: \: \: \: 21a + 47b = 110 \\ + \: 47a + 21b = 162 \\ - - - - - - - - - \\ 68a + 68b = 272 \\ \\ now \: divide \: this \: by \: 68 \\ \\ a + b = 4 \: \: \: \: ..........(3) \\ \\ now \: subsctracte \: equation \: 1 \: an d \: 2 \\ \\ \: \: \: \: 21a + 47b = 110 \\ - 47a + 21b = 162 \\ - - - - - - - - - \\ \\ - 26a + 26b = 52 \\ \\ \: \: \: \ a - b = - 2 \: \: \: \: ........(4) \\ \\ now \: substract \: equation \: 3 \: and \: 4 \\ \\ \: \: \: \: a + b = 4 \\ - a \: - b = - 2 \\ - - - - - - - - \\ 2b = 6 \\ b = \frac{6}{2} \\ \\ b = 3 \\ \\ now \: put \: b \: = 3 \: in \: equation \: 3 \\ \\ a + b = 4 \\ \\ a + 3 = 4 \\ \\ a = 4 - 3 \\ \\ a = 1 \: \\ \\ \\ now \: put \: the \: value \\ \frac{1}{x} = a \\ \frac{1}{x} = 1 \\ \\ x = 1 \\ \\ \frac{1}{y} = b \\ \\ \frac{1}{y} = 3 \\ \\ 3y = 1 \\ \\ y = \frac{1}{3}$