Question

1/x+1/y=11, 6/x-3/y=7 solve the following simultaneous equation​

Answer 1

$\huge\bold{Question:-}$

$\frac{1}{x} + \frac{1}{y} = 11$

$\frac{6}{x} - \frac{3}{y} = 7$

Solve the following simultaneous equation

$\huge\bold{Solution:-}$

Let

$\frac{1}{x} = a \: \: and \: \: \frac{1}{y} = b$

So,

$a + b \: = 11$________(1)

$6a - 3b = 7$_________(2)

$(a + b = 11) \times 3 = 3a + 3b = 33$

Solve (1) and (2)

$\: \: \: \: 3a + 3b = 33$

$( + )6a - 3b = 7$

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$9a = 26$

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$a = \frac{26}{9}$

$\frac{1}{x} = \frac{26}{9}$

$x = \frac{9}{26}$

Then,

$( \frac{9}{26} ) + ( \frac{1}{y} ) = 11$

$\frac{1}{y} = 11 - \frac{9}{26}$

$\frac{1}{y} = \frac{273}{26} = \frac{21}{2}$

$y = \frac{2}{21}$

Hope this is helpful