3x+2y=13 ------------------- (1)
x^2+xy-y^2 = 11 --------- (2)
from (1), x = (13-2y)/3. Substitute for this into (2).
(13-2y)^2/9 +y(13-2y)/3 - y^2 = 11
169 - 52y + 4y^2 + 39y - 6y^2 - 9y^2 = 99
-11y^2 - 13y + 70 = 0
(-11y - 35)(y - 2) = 0
y = -35/11, y = 2
x = 71/11, x = 3 using x = (13-2y)/3.