how to substitute machine numbers into an equation

I have a system of equations in which variables are indexed as:

8 x[1] + 2 y[1] == 2; 3 x[1] - 5 y[1] == 7; 

The solution obtained from my model is of the form:

sol = {{x[1.] -> 12/23, y[1.] -> -(25/23)}}; 

As seen, the variable index looks like a Machine Number (x[1.] and y[1.]). Therefore, I cannot map the sol onto the equations to check if they are satisfied.

I simply want the sol to be:

{{x[1] -> 12/23, y[1] -> -(25/23)}}; 

How can I get rid of the Machine Numbers to be the variable index?