This problem can be solved using a system of linear equations. Let x be the number of bracelets and y be the number of necklaces. We can write two equations based on the given information:
8x + 16y = 160 (total amount of gold used is 160 grams)
x + y = 12 (total number of bracelets and necklaces made is 12)
We can solve this system of equations by graphing the two lines and finding their point of intersection. The point of intersection will be the values of x and y that satisfy both equations.
To graph the first equation, we can rewrite it in slope-intercept form:
16y = -8x + 160
y = (-1/2)x + 10
To graph the second equation, we can rewrite it in slope-intercept form:
y = -x + 12
We can now graph these two lines and find their point of intersection:
From the graph, we can see that the point of intersection is (4, 8). Therefore, the jeweler made 4 bracelets and 8 necklaces.