document.write( "Question 1045709: How do I find X,Y,and Z?
\n" ); document.write( "X+y-2z=15
\n" ); document.write( "-x+2y+z=2
\n" ); document.write( "2x+3y-z=9
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #661201 by MathLover1(20849) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( " $\"x%2By-2z=15\"$ ..........(1)
\n" ); document.write( " $\"-x%2B2y%2Bz=2\"$ ..........(2)
\n" ); document.write( " $\"2x%2B3y-z=9\"$ ..........(3)\r
\n" ); document.write( "\n" ); document.write( "start with first two equations\r
\n" ); document.write( "\n" ); document.write( " $\"x%2By-2z=15\"$ ..........(1)
\n" ); document.write( " $\"-x%2B2y%2Bz=2\"$ ..........(2)
\n" ); document.write( "--------------------------------add\r
\n" ); document.write( "\n" ); document.write( " $\"x%2By-2z-x%2B2y%2Bz=15%2B2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"3y-z=17\"$ ......solve for $\"z\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"z=3y-17\"$ ................(1a)\r
\n" ); document.write( "\n" ); document.write( "go to\r
\n" ); document.write( "\n" ); document.write( " $\"-x%2B2y%2Bz=2\"$ ..........(2)......both sides multiply by $\"2\"$
\n" ); document.write( " $\"2x%2B3y-z=9\"$ ..........(3)
\n" ); document.write( "-----------------------------
\n" ); document.write( " $\"-2x%2B4y%2B2z=4\"$ ..........(2)
\n" ); document.write( " $\"2x%2B3y-z=9\"$ ..........(3)
\n" ); document.write( "--------------------------------------add\r
\n" ); document.write( "\n" ); document.write( " $\"-2x%2B4y%2B2z%2B2x%2B3y-z=4%2B9\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"7y%2Bz=13\"$ ......solve for $\"z\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"z=13-7y\"$ ................(1b)\r
\n" ); document.write( "\n" ); document.write( "from 1a and 1b we have\r
\n" ); document.write( "\n" ); document.write( " $\"3y-17=13-7y\"$ ..................solve for $\"y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"3y%2B7y=13%2B17\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"10y=30\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=30%2F10\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=3\"$ \r
\n" ); document.write( "\n" ); document.write( "now we can find $\"z\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"z=13-7y\"$ ................(1b)
\n" ); document.write( " $\"z=13-7%2A3\"$
\n" ); document.write( " $\"z=13-21\"$
\n" ); document.write( " $\"z=-8\"$ \r
\n" ); document.write( "\n" ); document.write( "now, go to $\"x%2By-2z=15\"$ ..........(1), substitute $\"y\"$ and $\"z\"$ and solve for $\"x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%2B3-2%28-8%29=15\"$
\n" ); document.write( " $\"x%2B3%2B16=15\"$
\n" ); document.write( " $\"x%2B19=15\"$
\n" ); document.write( " $\"x=15-19\"$
\n" ); document.write( " $\"x=-4\"$ \r
\n" ); document.write( "\n" ); document.write( "so, your solutions are:
\n" ); document.write( " $\"x=-4\"$
\n" ); document.write( " $\"y=3\"$
\n" ); document.write( " $\"z=-8\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );