Find the solution set of the equation {x^2+y^2=34
{x+y=2
Eq1: x^2 + y^2 = 34
Eq2: x + y = 2
x + y = 2
Y = 2 - x
In Eq1, replace Y with 2 - x.
x^2 + (2-x)^2 = 34
x^2 + 4 - 4x + x^2 = 34
2x^2 -4x + 4 = 34
2x^2 -4x - 30 = 0
Divide both sides by 2:
x^2 - 2 - 15 = 0
(x+3)(x-5) = 0
x+3 = 0
X = -3.
Y = 2- x = 2-(-3) = 5
x-5 = 0
X = 5.
Y = 2 - 5 = -3.
Solution sets: (-3,5),(5,-3).