Question 685215
From the second equation:

{{{x = 1-y}}}

Replace x in the first equation:

{{{(1-y)^2 + y^2 = 22}}}

{{{1 - 2y + y^2 + y^2 = 22}}}

{{{2y^2 -2y -21 = 0}}}

{{{y = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

{{{y = (2 +- sqrt((-2)^2-4*2*(-21)))/(2*2)}}}

{{{y = (1/2 +- sqrt(43)/2)}}}

First solution: {{{x=1/2-sqrt(43)/2}}} , {{{y=1/2+sqrt(43)/2}}}.

Second solution: {{{x=1/2+sqrt(43)/2}}} , {{{y=1/2-sqrt(43)/2}}}.