B=number of bracelets, N=number of necklaces.
B+N=9 (total number)
8B+20N=120 (total length of cord).
Matrix is:
⎛ 1 1 ⎞
⎝ 8 20 ⎠
Determinant Δ is 1×20-8×1=12.
Replace the first column with the numbers (total and cord length):
⎛ 9 1 ⎞
⎝ 120 20 ⎠
B-determinant ΔB=9×20-120×1=60, B=ΔB/Δ=60/12=5.
Replace the second column with the same numbers:
⎛ 1 9 ⎞
⎝ 8 120 ⎠
N-determinant ΔN=120-72=48, N=ΔN/Δ=48/12=4.
CHECK
B+N=5+4=9, 8B+20N=40+80=120 inches. This confirms 5 bracelets and 4 necklaces.