Question

1/x + 1/y =7;2/x +3/y =17​

Answer 1

Answer:

1 Solve for x in 1/x * 1/y = 7

y/7y-1

2 Substitute x=y/7y-1 * 2/x + 3/y =17

14y-1/y = 7

3 Solve for 14y+1/y = 17

x=1/3

4 Substitute y=1/3 * x=y/7y-1

x=1/4

5 )Therefore,

x=1/4

y=1/3

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Done

Answer 2

Answer:

$\frac{1}{x} + \frac{1}{y} = 7 \\ \frac{1}{x} = 7 - \frac{1}{y} \: .....(1) \\ \frac{2}{x} + \frac{3}{y} = 17 \\2(\frac{1}{x}) + \frac{3}{y} = 17 ...(2) \\ from \: equations \: (1) \: and \: (2) \\ 2(7 - \frac{1}{y}) + \frac{3}{y} = 17 \\ \therefore \: 14 - \frac{2}{y}+ \frac{3}{y} = 17 \\ \therefore\frac{1}{y} = 17 - 14 \\ \therefore\frac{1}{y} = 3 \: \\ \implies \huge \fbox{ y = \frac{1}{3} } \\ from \: equation \: (1) \\ \frac{1}{x} = 7 - 3 = 4 \\ \implies\frac{1}{x} = 4 \\ \implies \: \huge \fbox {x = \frac{1}{4} }$