just substitute y=2-x and you have
x^2 + (2-x)^2 = 34
2x^2 - 4x - 30 = 0
x^2 - 2x - 15 = 0
now it should be clear ...
Find the solution set of the equation
{x^2+y^2=34
{x+y=2
2 answers
y = -x +2
x^2 + (-x +2)^2 = 34
x ^2 + x^2 -2x -2x +4 = 34
2x^2 -4x + 4 = 34
2x^ -4x + 4 -34 = 34-34
2x^2 -4x - 30 = 0
2(x^2 -2x -15) =0
2(x-5)(x+3) =0
x -5 =0
x =5
x+ 3 = 0
x =-3
y = -3 ,5
(5,-3), (-3,5)
x^2 + (-x +2)^2 = 34
x ^2 + x^2 -2x -2x +4 = 34
2x^2 -4x + 4 = 34
2x^ -4x + 4 -34 = 34-34
2x^2 -4x - 30 = 0
2(x^2 -2x -15) =0
2(x-5)(x+3) =0
x -5 =0
x =5
x+ 3 = 0
x =-3
y = -3 ,5
(5,-3), (-3,5)