3x+2y=13 x^2+xy-y^2 = 11

Question

How to solve this simultaneous equation

Answer 1

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.