Remark
There are a number of ways you could do this. The most straight forward might be to simply multiply the second equation to get the answer.
Step One
Multiply the second equation by 2
2(2x^2 + 1/y^2 = 12) Remove the brackets.
4/x^2 + 2/y^2 = 12 * 2
4/x^2 + 2/y^2 = 24
Step Two
Add the new equation and the first original equation
1/x^2 - 2/y^2 = 1
4/x^2 + 2/y^2 = 24
5 / x^2 = 1 + 24
5/x ^2 = 25 Divide both sides by 5
1/x^2 = 5 Reciprocate the x^2 and the 5 (That means turn them upside down.
x^2 = 1/5
Take the square root of both sides.
x = +/- 1/sqrt(5) Rationalize the denominator.
Step 3
Place this answer in for x^2 to get y^2. and then y
1/(1/5) - 2/y^2 = 1
Interlude
You can use your calculator to see what 1/(1/5) is. Change the 1/5 to 0.2
1/0.2 = 5 Just put it in as
1
÷
0.2
=
You should get 5
Continued
5 - 2 / y^2 = 1 Subtract 5 from both sides.
- 2/y^2 = 1 - 5
-2 / y^2 = - 4 Divide both sides by - 2
1 / y^2 = -4/-2
1 / y^2 = 2 Now reciprocate both sides.
y^2 = 1/2 Take the square root.
y = +/- 1/sqrt(2) And rationalize the denominator
y = +/- sqrt(2) / 2 Done the same way as for the x.
There's only 1 there. I'll let you find it.