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?

• How are you solving the equations? If I simply write Solve[{8 x[1] + 2 y[1] == 2, 3 x[1] - 5 y[1] == 7}] I get {{x[1] -> 12/23, y[1] -> -25/23}} with no machine-precision numbers involved. May 6 '20 at 16:48
• @eyorble: You are right. I also get the same thing as you. But in my model (bold text in my message) the solution is produced by using x[1.], y[1.] etc. That is why I indicated that this solution is specific to my model. I solve the model by FindRoot[CGEmodel /. Flatten[{greekParamAssign, smallParamAssign}], initialValues, AccuracyGoal -> 3, PrecisionGoal -> 30] // N; May 6 '20 at 16:52
• You can do sol /. {x[n_] :> x[Rationalize[n]], y[n_] :> y[Rationalize[n]]}. May 6 '20 at 17:01
• Ok, assuming no other head-argument combinations appear that should not be tampered with, try sol /. head_[n_] :> head[Rationalize[n]]. May 6 '20 at 17:26
• Please show some effort on your own here, the matter is just to deal with a Sequence of arguments (n__) instead of a single one. You have not mentioned any of these details in your question about 1000 variables and several indices. May 6 '20 at 17:53

sol /. x_[n__?NumericQ] ->  :> x @@ Rationalize[{n}]

Of course, one can just Rationalize the whole thing, but that changes stuff on the RHS too, not only the indices.
A way of avoiding this problem all together is to not apply N to a whole expression containing variables indexed by numbers in the first place, but instead apply N only to the numerical stuff.
• First, I like to thank you for your code, which works as expected. Also, I will be careful about the use of N. My problem is solved... May 6 '20 at 20:05
• Another trick you can use is SetAttributes[x, NHoldAll]. This will prevent N from affecting arguments of x. So for example, N[x[1]] will just return x[1]. May 7 '20 at 14:36