The system of equations has two solutions: x equals y and x equals negative y.
To solve the system of equations 0 = y - 8x^(-2) and 0 = x - 8y^(-2), we can start by isolating one variable in terms of the other in each equation.
From the first equation, 0 = y - 8x^(-2), we can rearrange it to express y in terms of x:
y = 8x^(-2)
Similarly, from the second equation 0 = x - 8y^(-2), we can rearrange to express x in terms of y:
x = 8y^(-2)
Now, we can set these two expressions equal to each other, since they both equal zero:
8x^(-2) = 8y^(-2)
Simplifying by taking the reciprocal of both sides:
x^2 = y^2
Taking the square root of both sides:
x = ± y
So, the solutions to the system of equations are x = y and x = -y.