Question

solve for x and y
$\frac{x + y}{xy} = \frac{9}{2} \: and \: \frac{x - y}{xy} = \frac{3}{2}$
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Answer 1

Answer:

$x = \frac{2}{3}$

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

Step-by-step explanation:

$= > \frac{x + y}{xy} = \frac{9}{2} \\ = > 2x + 2y = 9xy - - - (i)$

And also,

$= > \frac{x - y}{xy} = \frac{3}{2} \\ = > 2x - 2y = 3xy - - - - (ii)$

Solving (i) and (ii)

${ = > (2x + 2y) - (2x - 2y) = 9xy - 3xy}$

$= > 2x + 2y - 2x + 2y = 6xy$

$= > 4y = 6xy$

$= > \frac{4y}{6y} = x$

$= > x = \frac{2}{3}$

Substituting x in (i) :-

$= > 2x + 2y = 9xy$

$= > 2(x + y) = 9xy$

$= > 2( \frac{2}{3} + y) = 9( \frac{2}{3} )y$

$= > 2( \frac{2 + 3y}{3} ) = \frac{18y}{3}$

$= > \frac{4 + 6y}{3} = \frac{18y}{3}$

$= > 4 + 6y = 18y$

$= > 4 = 18y - 6y$

$= > 4 = 12y$

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