Explanation:

Equation 1) x+y=2
Equation 2) x^2 +y^2 = 2
x+y=2 -> x=2-y (subtract y from both sides of eqn 1)
x^2 +y^2 = 2 -> (2-y)^2 +y^2 = 2 (substitute x from above into eqn 2)
(2-y)*(2-y) + y^2 = 2 (breaking out the square term)
4-2y-2y+y^2+y^2 = 2 (multiply each term of the parentheses)
4-4y+2y^2=2 (combine terms on left)
2y^2-4y+4=2 (rearrange terms on left)
2y^2-4y+2 =0 (subtract 2 from both sides)
y=1 (from quadratic formula)
x+1=2 (substitute y into equation 1)
x=1 (subtract 1 from both sides)
xy=1*1=1