document.write( "Question 477998: Solve the system\r
\n" ); document.write( "\n" ); document.write( "2x-3y+z=13
\n" ); document.write( "x+2y+3z=2
\n" ); document.write( "3x-y+z=12 \n" ); document.write( "

Algebra.Com's Answer #327520 by MathLover1(20849) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( " $\"2x-3y%2Bz=13\"$ .....1\r
\n" ); document.write( "\n" ); document.write( " $\"x%2B2y%2B3z=2\"$ .......2\r
\n" ); document.write( "\n" ); document.write( " $\"3x-y%2Bz=12\"$ .......3
\n" ); document.write( "-----------------------------\r
\n" ); document.write( "\n" ); document.write( " $\"2x-3y%2Bz=13\"$ .....1...solve for $\"z\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"z=-2x%2B3y%2B13\"$ ..........plug in 3\r
\n" ); document.write( "\n" ); document.write( "-----------------\r
\n" ); document.write( "\n" ); document.write( " $\"3x-y%2B%28-2x%2B3y%2B13%29=12\"$ .......3\r
\n" ); document.write( "\n" ); document.write( " $\"3x-y-2x%2B3y%2B13=12\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%2B2y=12-13\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%2B2y=-1\"$ ............solve for $\"x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=-2y-1\"$ .
\n" ); document.write( "----------------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"z=-2x%2B3y%2B13\"$ ...plug in $\"x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"z=-2%28-2y-1%29%2B3y%2B13\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"z=4y%2B2%2B3y%2B13\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"z=7y%2B15\"$ ....plug in 2 along with $\"x=-2y-1\"$ \r
\n" ); document.write( "\n" ); document.write( "--------\r
\n" ); document.write( "\n" ); document.write( " $\"x%2B2y%2B3z=2\"$ ....2\r
\n" ); document.write( "\n" ); document.write( " $\"%28-2y-1%29%2B2y%2B3%287y%2B15%29=2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-2y-1%2B2y%2B21y%2B45=2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"21y%2B44=2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"21y=2-44\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"21y=-42\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=-42%2F21\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=-2\"$ .............the solution .....plug in $\"x=-2y-1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=-2%28-2%29-1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=4-1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=3\"$ ...........the solution\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "now find $\"z\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"z=7y%2B15\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"z=7%28-2%29%2B15\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"z=-14%2B15\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"z=1\"$ ..........the solution\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "so, solutions are:\r
\n" ); document.write( "\n" ); document.write( " $\"x=3\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=-2\"$ and\r
\n" ); document.write( "\n" ); document.write( " $\"z=1\"$ \r
\n" ); document.write( "\n" ); document.write( "check:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"2x-3y%2Bz=13\"$ .....1\r
\n" ); document.write( "\n" ); document.write( " $\"2%283%29-3%28-2%29%2B1=13\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"6%2B6%2B1=13\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"13=13\"$ \r
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