If $x + y = 12$ and $x y = 27$ , find the values of $x$ and $y$ .

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Solution

$x + y = 12, - (1)$
$x y = 27 - (2)$
$y = 12 - x$
put in $(2)$
$x (12 - x) = 27$
$x^{2} - 12 x + 27 = 0$
$(x - 9) (x - 3) = 0$
x $= 9, 3$
for $x = 9$ , from $(1) y = 3$
for $x = 3$ , from $(1) y = 9$

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