# Numerical solution of a system of two exponential equations

I need to solve this two equations for x and y:

(sum ((i^2)e^(-x i - y i^2)), i = 1 to 6)/sum (e^(-x i - y i^2)), i = 1 to 6) = 12

(sum ((i)e^(-x i - y i^2)), i = 1 to 6)/sum (e^(-x i - y i^2)), i = 1 to 6) = 3


I've tried to use NSolve and find real solutions for x and y

NSolve[
{Sum[k E^(k^2*(-y) - k x), {k, 1, 6}]/Sum[E^(k^2*(-y) - k x), {k, 1, 6}] == 3,
Sum[k^2*E^(k^2*(-y) - k x), {k, 1, 6}]/Sum[E^(k^2*(-y) - k*x), {k, 1, 6}] == 12}, {x, y}, Reals]


but I got the message:

NSolve: Requested precision R is not a machine-sized real number between MinPrecision and MaxPrecision"

How do I proceed?

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• Could you add your code, which would help people find the problem? Oct 25, 2018 at 1:22
• NSolve[{Sum[kE^(k^2*(-y) - kx), {k, 1, 6}]}/{Sum[E^(k^2*(-y) - kx), {k, 1, 6}]} == 3, {x, y}, {Sum[k^2*E^(k^2*(-y) - kx), {k, 1, 6}]}/{Sum[E^(k^2*(-y) - k*x), {k, 1, 6}]} == 12, {x, y}, Reals] Oct 25, 2018 at 1:34

A few problems with your code:

1. Curly braces {} can't be used as parentheses ().
2. You need a space or * between k and x to multiply them, otherwise Mathematica thinks it's a new variable kx.
3. The syntax of NSolve has a list of equations as the first argument, and a list of unknowns -- {x,y} here -- as the second argument.

The following seems to work:

NSolve[{
Sum[k E^(k^2*(-y) - k x), {k, 1, 6}]/Sum[E^(k^2*(-y) - k x), {k, 1, 6}] == 3,
Sum[k^2*E^(k^2*(-y) - k x), {k, 1, 6}]/Sum[E^(k^2*(-y) - k*x), {k, 1, 6}] == 12},
{x, y}, Reals]
(* {{x -> 0.440365, y -> -0.0399564}} *)