2x^2 - 4y^2 = 22
-4y^2 = -2x^2 + 22
y^2 = (1/2)x^2 - 11/2
x^2 - 3y^2 = 6
-3y^2 = -x^2 + 6
y^2 = (1/3)x^2 - 2
(1/2)x^2 - 11/2 = (1/3)x^2 - 2
3x^2 - 33 = 2x^2 - 12
x^2 - 33 = -12
x^2 = 21
x = +- sqrt(21)
21 - 3y^2 = 6
-3y^2 = -15
y^2 = 5
y = +-sqrt(5)
x = sqrt(21) or -sqrt(21) and y = sqrt(5) or -sqrt(5)
Four solutions:
x = sqrt(21), y = sqrt(5)
x = sqrt(21), y = -sqrt(5)
x = -sqrt(21), y = sqrt(5)
x = -sqrt(21), y = -sqrt(5)