Question 1177406

{{{(x-1)^2+(y+1)^2 = 50}}}................1)
{{{-x+y = -10}}}........................2)
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{{{(x-1)^2+(y+1)^2 = 50}}}................1) expand

{{{x^2-2x+1+y^2+2y+1 = 50}}}

{{{x^2-2x+1+y^2+2y+1 -50=0}}}

{{{x^2-2x+y^2+2y -48=0}}}............1a


{{{-x+y = -10}}}........................2), solve for {{{y}}}

{{{y =x -10}}}........................, substitute in 1a

{{{x^2-2x+(x -10)^2+2(x -10) -48=0}}}

{{{x^2-2x+x^2 -20x+100+2x -20-48=0}}}

{{{2x^2 -20x+32=0}}}....simplify

{{{x^2 -10x+16=0}}}

{{{(x - 8) (x - 2) = 0}}}

=> x=8 or x=2

go to
{{{-x+y = -10}}}........................2), substitute {{{x=8}}}

{{{-8+y = -10}}}
{{{y = -10+8}}}
{{{y = -2}}}

or

{{{-x+y = -10}}}........................2), substitute {{{x=2}}}

{{{-2+y = -10}}}
{{{y = -10+2}}}
{{{y = -8}}}

Solutions:
{{{x=8}}},{{{y = -2}}}
{{{x=2}}}, {{{y = -8}}}