document.write( "Question 471629: x+y+z=6
\n" ); document.write( "2x-y+z=8
\n" ); document.write( "x-2y-z=-19\r
\n" ); document.write( "\n" ); document.write( "I need help solving these systems of equations. \n" ); document.write( "

Algebra.Com's Answer #323462 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!
\r
\n" ); document.write( "\n" ); document.write( " $\"x%2By%2Bz=6\"$ .......1\r
\n" ); document.write( "\n" ); document.write( " $\"2x-y%2Bz=8\"$ ...........2\r
\n" ); document.write( "\n" ); document.write( " $\"x-2y-z=-19\"$ ......3
\n" ); document.write( "--------------------------------\r
\n" ); document.write( "\n" ); document.write( " $\"x%2By%2Bz=6\"$ .......1
\n" ); document.write( " $\"x-2y-z=-19\"$ ......3......subtract 3 from 1 to eliminate $\"x\"$
\n" ); document.write( "------------------------\r
\n" ); document.write( "\n" ); document.write( " $\"x-x%2By-%28-2y%29%2Bz-%28-z%29=6-%28-19%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y%2B2y%2Bz%2Bz=6%2B19\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"3y%2B2z=25\"$ .............a\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x%2By%2Bz=6\"$ .......1\r
\n" ); document.write( "\n" ); document.write( " $\"2x-y%2Bz=8\"$ ...........2
\n" ); document.write( "--------------------------......subtract 2 from 1 to eliminate $\"z\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x-2x%2By-%28-y%29%2Bz-z=6-8\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"-x%2By%2By=-2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-x%2B2y=-2\"$ .............b\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"3y%2B2z=25\"$ .............a.....solve for $\"z\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"2z=25-3y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"z=25%2F2-3y%2F2\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x%2By%2Bz=6\"$ .......1..plug in $\"z\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%2By%2B25%2F2-3y%2F2=6\"$ .........c\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "now take $\"-x%2B2y=-2\"$ .....b ...solve for $\"x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2y%2B2=x\"$ .......plug it in c\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x%2By%2B25%2F2-3y%2F2=6\"$ .........c\r
\n" ); document.write( "\n" ); document.write( " $\"2y%2B2%2By%2B25%2F2-3y%2F2=6\"$ ....solve for $\"y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"3y%2B2%2B25%2F2-3y%2F2=6\"$ ....both sides multiply by $\"2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"3y%2A2%2B2%2A2%2B%2825%2F2%292-%283y%2F2%292=6%2A2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"6y%2B4%2B25-3y=12\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"3y%2B29=12\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"3y=12-29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"3y=-17\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=-17%2F3\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=-5.7\"$ \r
\n" ); document.write( "\n" ); document.write( "now plug it in .....b and find $\"x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-x%2B2%28-5.7%29=-2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-x-11.4=-2\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"-x=-2%2B11.4\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-x=9.4\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=-9.4\"$ ........now find $\"z\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"z=25%2F2-3y%2F2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"z=25%2F2-3%28-5.7%29%2F2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"z=12.5%2B8.55\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"z=21.05\"$ \r
\n" ); document.write( "\n" ); document.write( "so, solutions are:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x=-9.4\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=-5.7\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"z=21.05\"$ \r
\n" ); document.write( "\n" ); document.write( "check:\r
\n" ); document.write( "\n" ); document.write( " $\"x%2By%2Bz=6\"$ .......1\r
\n" ); document.write( "\n" ); document.write( " $\"-9.4-5.7%2B21.05=6\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-15.1%2B21.05=6\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"5.95=6\"$ .....round it\r
\n" ); document.write( "\n" ); document.write( " $\"6=6\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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