SOLUTION: Please help. I have been working this problem for three days and keep getting different answers. My downfall is the signs, I think. Use Cramer's Rule to solve the linear system

Question 83015: Please help. I have been working this problem for three days and keep getting different answers. My downfall is the signs, I think.
Use Cramer's Rule to solve the linear system
4x + 3y - z = 12
x - 3y + 3z = 14
3x + y + z = 18
I know that D = 4 3 -1
1 -3 3
3 1 1
Dx= 12 3 -1
14 -3 3
18 1 1
Dy= 4 12 -1
1 14 3
3 18 1
I understand how to proceed but the signs are giving me a headache. I am at the point that I just want to view the right answer in its entirity to see where I am going wrong. Thanks in advance.
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
your setup looks OK

D=-12+27-1-9-12-3=-10 ... Dx=-36+162-14-54-36-42=-20 ... Dy=56+108-18-(-42)-216-12=-40
Dz=-216+126+12+108-56-54=-80

so, by Cramer, x=2, y=4, and z=8
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