Question

Sum and product are -155 and 350. Numbers which satisfy this condition (factorisation method)

Answer 1

Our two equations are:

x+y=16(1)(1)x+y=16

xy=55(2)(2)xy=55

Rewriting equation (1) in terms of just y=y= something, we get:

y=16−xy=16−x

Substituting this into equation (2) leaves us:

x(16−x)=55x(16−x)=55

16x−x2=55⟹x=5  or  1116x−x2=55⟹x=5  or  11

which can be easily seen by factoring or using the quadratic formula. It follows that y=11|x=5y=11|x=5 and y=5|x=11y=5|x=11.
Thus your solutions in terms of (x,y)(x,y) are (5,11)(5,11) and (11,5)(11,5).