Question 331483
<pre><b>

{{{system(x+y+z=-1,
x-y+3z=-17,
2x+y+z=-2)}}}

1. Pick a letter to eliminate and two equations that contain it to
   eliminate it from.

I will pick y to eliminate, and the first two equations to eliminate it
from:

{{{system(x+y+z=-1,
x-y+3z=-17)}}}

Add corresponding terms and the y's drop out:

{{{2x+4z=-18}}}

Since all the coefficients are equal, do let's divide every term by 2

{{{x+2z=-9}}}

2. Eliminate the same letter, y, from two equations that contain it to
   eliminate it, but this time use the equation that you haven't used
   yet

I will eliminate y from the second and third equations to eliminate it
from:

{{{system(
x-y+3z=-17,
2x+y+z=-2)}}}

Add corresponding terms and the y's also drop out:

{{{3x+4z=-19}}}

Now we have two equations in two unknowns

{{{system(x+2z=-9,3x+4z=-19)}}}

I will eliminate z by multiplying the first equation by -2:

{{{system(-2x-4z=18,3x+4z=-19)}}}

Add them term by term and the z's drop out:

{{{x=-1}}}

Substitute -1 for x in one of those equations, say

{{{x+2z=-9}}}

{{{-1+2z=-9}}}

{{{2z=-8}}}

{{{z=-4}}}

Now substitute -4 for z and -1 for x in one of the
original equations, say this one

{{{x+y+z=-1}}}

{{{-1+y+(-4)=-1}}}

{{{-1+y-4=-1}}}

{{{-5+y=-1}}}

{{{y=4}}}

So the solution is

(x,y,z) = (-1,4,-4}}}

Edwin </pre>