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Law of Reciprocal

Solve: x-2y=...

Question

Solve:
$x - 2 y = 1; 2 x - 2 y + 5 = 0$

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Solution

$x - 2 y = 1$
$2 x - 2 y = - 5$
$\Rightarrow 2 x - 2 y - x + 2 y = - 5 - 1$
$\Rightarrow x = - 6$
Put $x = - 6$ in $x - 2 y = 1$ we get
$\Rightarrow - 6 - 2 y = 1$
$\Rightarrow - 2 y = 1 + 6 = 7$
$\Rightarrow y = \frac{- 7}{2}$
$∴ x = - 6$ , $y = \frac{- 7}{2}$

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x + 2 y + 3 z = 1; 2 x + 5 y + 6 z = 2; 3 x + 7 y + 8 z = 4

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x + 2 y = 0

x - 2 y = 0

x \neq 0, y \neq 0 :

\frac{1}{2 (x + 2 y)} + \frac{5}{3 (3 x - 2 y)} = \frac{- 3}{2} \frac{5}{4 (x + 2 y)} - \frac{3}{5 (3 x - 2 y)} = \frac{61}{60}

x - 2 y = 0 a n d 3 x - y = 5

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