If 2x+3y=14 and 2x-3y=2, find the value of xy.

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Solution

$2 x + 3 y = 14, 2 x - 3 y = 2$
Adding :
$2 x + 3 y = 14$
$2 x - 3 y = 2$
__________
$4 x = 16$
$x = 4$
$∴ x y = 4 \times 2$
$= 8$
$2 \times 4 + 3 y = 14$
$8 + 3 y = 14$
$3 y = 6$
$y = 2$

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