The first approach doesn't have two sentences
And anyone can make it work.
Is a phrase, as it expresses an incomplete idea.
And is a conjunction, used to join two similar things together (similar ideas, or similar sentence structures).
So you are right to combine the two, because you have only one sentence and a phrase.
It will be the system that anyone can make work.
Is a correct, fully formed sentence. It is clear, but you are right, it isn't a sentence that is natural. That's because of a few reasons.
- You use the word
it before you introduce what it describes. The general rule is describe the item clearly first, then use the word it as a replacement for describing it again.
- You have confused the direct object (the noun receiving the action) with the subject (the noun performing the action.
The first problem is fixed by changing
It will be the system that anyone can make work
The system will be one that anyone can make work
And with this improvement, the second problem becomes easier to notice. "The system" isn't doing anything, but "anyone" is doing something. This means that "anyone" is the proper subject, not "the system".
Anyone can make the system work.
Which is even better, but "make the system work" is vague. We don't know if they are fixing the system or just using the system to perform work. So the final improvement might be.
Anyone can repair the system.
Anyone can use the system.
Using your verbs to express actions, instead of existence, will help you avoid problems of switching the direct object of a sentence for the subject.