Math
posted by Alexander on .
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 + (2x)^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)(x5) = 0
x+3 = 0
X = 3.
Y = 2 x = 2(3) = 5
x5 = 0
X = 5.
Y = 2  5 = 3.
Solution sets: (3,5),(5,3).