2/x2 + 1/y2 = 11, 4/x2  2/y2 = 14 solve for x and y

2/x^2 + 1/y^2 = 11
4/x^2  2/y^2 =  14
1/x^2 = a, 1/y^2 = b
2*a + b = 11, multiply by 2
4*a  2*b =  14
4*a + 2*b = 22
4*a  2*b =  14

8*a = 8
a = 1
2*a + b = 11
b = 9
1/x^2 = a, 1/y^2 = b
1/x^2 = 1, x^2 = 1, x = ± 1
1/y^2 = 9
y^2 = 1/9, y = ± 1/3
4/x^2  2/y^2 =  14
1/x^2 = a, 1/y^2 = b
2*a + b = 11, multiply by 2
4*a  2*b =  14
4*a + 2*b = 22
4*a  2*b =  14

8*a = 8
a = 1
2*a + b = 11
b = 9
1/x^2 = a, 1/y^2 = b
1/x^2 = 1, x^2 = 1, x = ± 1
1/y^2 = 9
y^2 = 1/9, y = ± 1/3

MULTIPLY BY 2 EQUATION 1
4/ x^2 + 2/ y^2 = 22
4/x^2 2 / y^2 = 14
ADD
8/x^2 = 8
x^2 = 1
x = +1 OR 1 ANSWER
1/y^2 = 9
9y^2 = 1
y^2 = 1/9
y = + 1/3 Or  1/3 ANSWER
4/ x^2 + 2/ y^2 = 22
4/x^2 2 / y^2 = 14
ADD
8/x^2 = 8
x^2 = 1
x = +1 OR 1 ANSWER
1/y^2 = 9
9y^2 = 1
y^2 = 1/9
y = + 1/3 Or  1/3 ANSWER

u=1/x2 v=1y2
2u+v=11
4u2v=14
4u+2v=22
4u2v=14
_________
8u=8
u=1
2(1)+v=11
v=9
x2=1 y2=1/9
2u+v=11
4u2v=14
4u+2v=22
4u2v=14
_________
8u=8
u=1
2(1)+v=11
v=9
x2=1 y2=1/9