Question 151163
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