Question 711727
{{{y-x=6}}} and {{{xy=-223+x^2+y^2}}}


Using the simpler equation, y=x+6.  Substitute into the quadratic equation.
{{{x(x+6)=-223+x^2+(x+6)^2}}}
{{{x^2+6x=x^2+(x^2+12x+36)-223}}}
{{{x^2+6x=2x^2+12x-187}}}
{{{0=x^2+6x-187}}}


Solution to quadratic formula makes the most sense because looking for several factorizations for 187 is not efficient in time. (Unless you just SEE IT).


Intentionally using the positive root,
{{{x=(-6+sqrt(6^2-4(-187)))/2}}} = 11,  {{{highlight(x=11)}}}
Based on that and required difference, {{{highlight(y=17)}}}.