Question

Solve the following simultaneous equations:
1/x+1/y=8 , 4/x-2/y=2​

Answer 1

Let 1/x = p and 1/y = q

$\frac{1}{x} + \frac{1}{y} = 8 \\ p + q = 8 - - - - - > (1) \\ \\ \frac{4}{x} - \frac{2}{y} = 2 \\ 4p - 2q = 2 \\ 2p - q = 1 - - - - - > (2) \\ \\ (1) + (2) \\ p + 2p + q - q = 8 + 1 \\ 3p = 9 \\ p = 3 \\ \\ 3 + q = 8 \\ q = 5$

Therefore 1/x = p = 3 and 1/y = q = 5

x = ⅓ and y = 1/5

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