Help with Simultaneous Equations

I was doing good then i saw this question i've re-written it 2 times already. Why is the answer...
(100/13, -45/13)

x^2+y^2-2x+6y-35=0
2x+3y=5

x^2+y^2-2x+6y-35=0
Solve the second equation for x
2x + 3y = 5
x = (5-3y)/2

((5-3y)/2)^2 + y^2 - 2(5-3y)/2 + 6y-35 = 0
(25-30y+9y^2)/4+y^2 - (5-3y) + 6y-35 = 0
25-30y+9y^2 + 4y^2 - 20 + 12y + 24y -140=0
13y^2 +6y -135 = 0
(13y+45 )(y-3)=0
y = -45/13 or 3
=>
2x + 3(-45/13) = 5
2x = 5+135/13
2x = 200/13
x = 100/13, y = -45/13
OR
2x +3(3) = 5
x = -4/2 = -2, y = 3

kk