A²+Y²=34,a+y=2

Answer 1

from the 2nd: a = 2-y
into the 1st:
(2-y)^2 + y^2 = 34
4 - 4y + y^2 + y^2 = 34
2y^2 - 4y - 30 = 0
y^2 - 2y - 15 = 0

continue, it factors nicely