said by whizkid3:Here's my solution. Note that I didn't use matrices with Cramer's rule, as I was too lazy - just algebra:
(Compound/Forumla/Atomic Weight)
Tetrasulphur tetranitride/S4N4/184
Sulphur hexaflouride/SF6/146
Dinitrogen tetraflouride/N2F4/104
Use a linear system and Cramer's rule to find the atomic weights of sulphur (S), nitrogen (N), and flourine (F).
4S + 4N =184
S + 6F = 146
2N + 4F = 104
S = 46 - N
46 - N + 6F = 146
N = -100 + 6F
4F = 104 - 2(- 100 + 6F)
4F = 104 +200 - 12F = 304 - 12F
F = 76 - 3F
4F = 76
F = 19
N = -100 +6(19)
N = 14
S = 46 - N = 46 - 14
S = 32
I set up the same 3 equations and then used matrices and Cramer's Rule. I just plugged the matrices into a graphing calculator and came up with the answer because finding the determinant of each matrix can take a while.
