+52 https://web2.0calc.com/questions/if-x-y-satisfies-the-simultaneous-equations-where
+129850 3xy -4x^2 -36y +48 x = 0
3xy - 36y - 4x^2 + 48x = 0
3y ( x - 12) - 4x(x - 12) = 0
(x - 12) ( 3y - 4x) = 0
x = 12 and 3y = 4x ⇒ y = (4/3)x
Using the first solution in the second equation, we have
x^2 - 2y^2 = 16
12^2 - 2y^2 = 16
12^2 - 16 = 2 y^2
144 - 16 = 2y^2
128 = 2y^2
64 = y^2
y = 8 and -8
So (12, 8) and (12 , -8) are solutions
And
x^2 - 2 [( 4/3)x]^2 = 16
x^2 - (32/9)x^2 = 16
(-23/9)x^2 = 16
x^2 = 16 (-9 / 23)
x^2 = -144/23
So
x = -12i / sqrt (23) and x = 12i / sqrt (23)
And y = (4/3) (-12i) / sqrt 23 = -16i/sqrt 23 and 16i / sqrt (23)
So
( -12i/sqrt 23, -16i/sqrt 23) and ( 12i/sqrt 23 , 16i/sqrt 23) are also solutions
