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Let's use the variables B for the number of bracelets made and N for the number of necklaces made.
From the problem, we know that the amount of gold used can be determined by multiplying the number of bracelets made by 5 and the number of necklaces made by 16, so we have the equation:
5B + 16N = 130
We also know that the number of bracelets made is 5 more than the number of necklaces made, so we have the equation:
B = N + 5
Thus, the system of equations that could be used to determine the number of bracelets made and the number of necklaces made is:
5B + 16N = 130
B = N + 5