document.write( "Question 831765: 1/x + 2/y - 4/z = 1
\n" ); document.write( " 2/x + 3/y + 8/z = 0
\n" ); document.write( "-1/x + 9/y + 10/z = 5\r
\n" ); document.write( "\n" ); document.write( "then solve x, y and z values. \n" ); document.write( "

Algebra.Com's Answer #501621 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"u=1%2Fx\"$ , $\"v=1%2Fy\"$ , $\"w=1%2Fz\"$
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\n" ); document.write( "1. $\"u%2B2v-4w=1\"$
\n" ); document.write( "2. $\"2u%2B3v%2B8w=0\"$
\n" ); document.write( "3. $\"-u%2B9v%2B10w=5\"$
\n" ); document.write( "Use Gaussian elimination.
\n" ); document.write( "Multiply eq. 1 by 2 and subtract from eq. 2.
\n" ); document.write( " $\"2u%2B4v-8w-2u-3v-8w=2\"$
\n" ); document.write( "4. $\"v-16w=2\"$
\n" ); document.write( "Add eq. 1 and eq. 3,
\n" ); document.write( " $\"u%2B2v-4w-u%2B9v%2B10w=1%2B5\"$
\n" ); document.write( "5. $\"11v%2B6w=6\"$
\n" ); document.write( "Now multiply eq. 4 by 11 and subtract from eq. 5,
\n" ); document.write( " $\"11v-176w-11v-6w=22-6\"$
\n" ); document.write( " $\"-182w=16\"$
\n" ); document.write( " $\"w=-16%2F182\"$
\n" ); document.write( " $\"w=-8%2F91\"$
\n" ); document.write( "Now back substitute,
\n" ); document.write( " $\"v-16w=2\"$
\n" ); document.write( " $\"v-16%28-8%2F91%29=2\"$
\n" ); document.write( " $\"v%2B128%2F91=182%2F91\"$
\n" ); document.write( " $\"v=54%2F91\"$
\n" ); document.write( "And finally,
\n" ); document.write( " $\"u%2B2v-4w=1\"$
\n" ); document.write( " $\"u%2B2%2854%2F91%29-4%28-8%2F91%29=1\"$
\n" ); document.write( " $\"u%2B108%2F91%2B32%2F91=91%2F91\"$
\n" ); document.write( " $\"u%2B140%2F91=91%2F91\"$
\n" ); document.write( " $\"u=-49%2F91\"$
\n" ); document.write( " $\"u=-7%2F13\"$
\n" ); document.write( "Last step,
\n" ); document.write( " $\"u=1%2Fx=-7%2F13\"$
\n" ); document.write( " $\"highlight%28x=-13%2F7%29\"$
\n" ); document.write( " $\"v=1%2Fy=54%2F91\"$
\n" ); document.write( " $\"highlight%28y=91%2F54%29\"$
\n" ); document.write( " $\"w=1%2Fz=-8%2F91\"$
\n" ); document.write( " $\"highlight%28z=-91%2F8%29\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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