What code can I use to get a system of equations to individually add up to a large sum?

Note: They can not all be equal to each other. I could guess but it'd be repitive and tedious and easy to make a mistake. Its for a school puzzle I am making.

[Steven Lord]

Your problem statement isn't really that clear on what your ultimate goal is.

What do the equations in this system represent?

What are the limitations on those equations (linear, polynomials of degree no higher than N, trig functions allowed, whatever special function you want to include allowed, etc.?)

Why are you adding the equations? Are you trying to do something like a polynomial magic square (like the magic function returns but with functions of x?)

What type of puzzle are you making?

[John D'Errico]

As Steven has said, this is way to vague for any answer.

If I had to guess, you are looking for something like an integer partition of a number. But you need to recognize that the number of ways will be huge that you can write a number even as small as 100 as a sum of distinct integers, none of which are the same.

[Jon]

Just a style suggestion, it is better to have a brief description of the nature of your problem in the title, and then provide more details in the body of your question. Here you ended up with a very long title, and no body. So the title was too long and there still wasn't enough of a description for people to help you. So, next time, please try for a shorter title, and longer description in the body.