Question 1134370
{{{system(3x-y-2z= 18,
2x+y-2z=15,
x+3y-z=10)}}}
<pre>
Pick a pair of equations and a letter to eliminate.
[Note: There are 6 different ways to start, all correct!]

I will pick the first two equations and y to eliminate,
because it happens to be the easiest because all you have to
do is add them and y will be eliminated:

{{{system(3x-y-2z= 18,
2x+y-2z=15)}}}
{{{matrix(1,5,    "",5x,"","",-4z=33)}}} 

Now pick a different pair of equations and eliminate the
SAME letter eliminated first. 
[Note: we have to pick one of the same equations again, but
we must pick the third equation this time.]

So I will pick the first and third equations and y to eliminate:

{{{system(3x-y-2z= 18,
x+3y-z=10)}}}

To eliminate y we multiply the first equation through by 3

{{{system(9x-3y-6z= 54,
""x+3y-z=10)}}}
{{{matrix(1,5,    "",10x,"","",-7z=64)}}} 

Now we have 2 equations in 2 letters to solve:

{{{system(5x-4z=33,10x-7z=64)}}}

We can eliminate x by multiplying the first equation through by -2

{{{system(-10x+8z=-66,""+10x-7z=""+64)}}} 
        {{{z=-2}}}

Substitute that in 

{{{5x-4z=33}}}
{{{5x-4(-2)=33}}}
{{{5x+8=33}}}
{{{5x=25}}}
{{{x=5}}}

Substitute z=-2 and x=5 in any one of the original equations:

{{{3x-y-2z= 18}}}
{{{3(5)-y-2(-2)=18
{{{15-y+4=18}}}
{{{19-y=18}}}
{{{-y=-1}}}
{{{y=1}}}

Answer: (x,y,z) = (5,1,-2)

Edwin</pre>