Question 43021
<pre>
OK #1:
<font color=orange>8x-y+z=41</font>
<font color=green>4x+2y-3z=42</font>
<font color=blue>x-3y+2z=-11</font>

<font color=orange>8x-y+z=41</font>We want to isolate a variable, -41 and +y on both sides.
<font color=orange>8x+z-41=y</font>That's as far as we go with the 1st equation.
<font color=green>4x+2y-3z=42</font>Here's the magic.  You see the y?  We're going to replace it according to <br>our final equation preceeding.
<font color=green>4x+2<font color=orange>(8x+z-41)</font>-3z=42</font>simplify, don't lose your head yet!
<font color=green>4x+16x+2z-82-3z=42</font>keep going!
<font color=green>20x-z-82=42</font> OK back to magic, we have to isolate another variable.  +z and -42 on <br>both sides.
<font color=green>20x-124=z</font>that's as far as the second equation goes.
<font color=blue>x-3y+2z=-11</font>Again, replace z with correspondant on preceeding equation.  <br><tt>WAIT!</tt> We have another variable we can replace, Y.  Let's do that..  [If you haven't <br>gone completely insane from this crazy process keep it 2gether just a little longer =P]
<font color=blue>x-3<font color=orange>(8x+z-41)</font>+2<font color=green>(20x-124)</font>=-11</font>Having fun yet?  SIMPLIFY
<font color=blue>x-24x-3z+123+40x-248=-11</font>keep going..:D
<font color=blue>17x-3z-125=-11</font>Have I lost you yet?  If I haven't, I'll give it one more try.  Replace <br>z with its equivalent ;)
<font color=blue>17x-3<font color=GREEN>(20x-124)</font>-125=-11</font>If you're still here we're almost done.  SIMPLIFY
<font color=blue>17x-60x+372-125=-11</font>simplify!
<font color=blue>-43x+247=-11</font>(; our first solvable equation!  -247 both sides
<font color=blue>-43x=-258</font>divide by -43
<font color=blue>x=6</font>PHEW! an even number!  now plug it in to various
equations..  SPECIFICALLY the equation with X and another variable:
<font color=green>z=20x-124</font> replace x with equivalent, 6:
<font color=green>z=20<font color=blue>(6)</font>-124</font>solve:
<font color=green>z=120-124=-4</font>.  Plug that in the equation with z, x, and another variable:
<font color=orange>8x+z-41=y</font> plug in 6 for x and -4 for z.
<font color=orange>8<font color=green>(6)</font>+<font color=blue>(-4)</font>-41=y</font>this is fun, huh?  solve:
<font color=orange>y=48-4-41=3</font>sarcastic woohoo.

WOOOO!!!!! WE'RE DONE!!
<font color=blue>x=6</font>
<font color=green>z=-4</font>
<font color=orange>y=3</font>

I would <sub><font size=-6>not</font></sub> love to do the other problems with you, but will not for a few reasons.  <br>The first being my concern for my own sanity, the second my concern for your own, <br>and the last, so you can see if you yourself understand how to solve them.  try it <br>on your own!  EMAIL or IM me for questions.. good luck.</pre>