Question 1094464
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Although the solution can be discovered by 5-10 seconds of observation, here are the steps needed to solve it procedurally (so you'll know how to solve problems when the solution is not so obvious):

x + y = -5  (1)  —> y = -5 - x
xy = 6   (2)

Substitute for y from (1) in (2):  
x(-5-x) = 6
{{{-5x -x^2 = 6 }}}    
{{{ x^2 + 5x + 6 = 0 }}}
{{{ (x+3)(x+2) = 0 }}}
{{{ x=-3 }}} and {{{ x=-2 }}}

x=-3 ==> y = -5 - (-3) = -2
x=-2 ==> y = -5 - (-2) = -3   (so this case is just the x & y values swapped, we can accept either one since x and y have no special meaning here)

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Ans: The numbers satisfying the given criteria are {{{ highlight(-2 ) }}} and {{{ highlight(-3) }}}
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Check:  -2 - 3 = -5  (ok)
     and  (-2)*(-3) = 6  (ok)