document.write( "Question 57957: Solve each system in three variables form\r
\n" ); document.write( "\n" ); document.write( "x+2y-z=5
\n" ); document.write( "-3x-2y-3z=11
\n" ); document.write( "4x+4y+5z=-18 \n" ); document.write( "
Algebra.Com's Answer #39919 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
x + 2y - z = 5
\n" ); document.write( "-3x - 2y- 3z = 11
\n" ); document.write( " 4x + 4y + 5z = -18
\n" ); document.write( ":
\n" ); document.write( "Looking at this we can see that if we mult the 1st equation by -1, something
\n" ); document.write( "wonderful will happen: (x & y are eliminated!)
\n" ); document.write( "-x - 2y + z = -5
\n" ); document.write( "-3x -2y - 3z = 11
\n" ); document.write( "+4x +4y + 5z = -18
\n" ); document.write( "-------------------- add all three equations:
\n" ); document.write( "0x + 0y + 3z = -12
\n" ); document.write( " z = -12/3
\n" ); document.write( " z = -4
\n" ); document.write( ":
\n" ); document.write( "Now take the 1st two equations, substitute -4 for z:
\n" ); document.write( "x + 2y -(-4) = 5
\n" ); document.write( "3x - 2y -3(-4) = 11
\n" ); document.write( ":
\n" ); document.write( "we have:
\n" ); document.write( "x + 2y + 4 = 5
\n" ); document.write( "3x -2y + 12 = 11
\n" ); document.write( "----------------- add, eliminates y, leaves us with x
\n" ); document.write( "4x + 0y + 16 = 16
\n" ); document.write( " 4x = 16 - 16
\n" ); document.write( " 4x = 0
\n" ); document.write( " x = 0
\n" ); document.write( ":
\n" ); document.write( "Find y using the 1st equation:
\n" ); document.write( "0x + 2y + 4 = 5
\n" ); document.write( " 2y = 5 - 4
\n" ); document.write( " 2y = 1
\n" ); document.write( " y = 1/2
\n" ); document.write( ":
\n" ); document.write( "Check our solutions x=0, y=.5, z=-4 in the 2nd and 3rd equations\r
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