SOLUTION: Could you please help me solve this system of equations? 5x+3y+z=-13 x-3y+2z=1 14x-2y+3z=-16

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Question 151163: Could you please help me solve this system of equations?
5x+3y+z=-13
x-3y+2z=1
14x-2y+3z=-16
Answer by nabla(475) About Me  (Show Source):
You can put this solution on YOUR website!
From R1:
z=-13-3y-5x
Put this in R2:
x-3y+2(-13-3y-5x)=1
-9x-9y=27
x+y=-3
y=-3-x
Redo z
z=-13-3(-3-x)-5x
z=-4-2x
Now use y and z in the last equation:
14x-2(-3-x)+3(-4-2x)=-16
10x=-10
x=-1
then
y=-3+1=-2
and
z=-4+2=-2
So our solution set is {-1,-2,-2}.
check:
-5-6-2=-13
-1+6-4=1
-14+4-6=-16
Yes