document.write( "Question 1058261: Please help me solve this 3 variable system:
\n" ); document.write( "x+y+z=8
\n" ); document.write( "x-y/3+(4/3)z=7
\n" ); document.write( "3z-3y-2x=7\r
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Algebra.Com's Answer #673311 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
(1) $\"+x+%2B+y+%2B+z+=+8+\"$
\n" ); document.write( "---------------------
\n" ); document.write( "(2) $\"+x+-+y%2F3+%2B+%284%2F3%29%2Az+=+7+\"$
\n" ); document.write( "(2) $\"+3x+-+y+%2B+4z+=+21+\"$
\n" ); document.write( "----------------------------
\n" ); document.write( "(3) $\"+-2x+-+3y+%2B+3z+=+7+\"$
\n" ); document.write( "----------------------------
\n" ); document.write( "Multiply both sides of (1) by $\"+2+\"$
\n" ); document.write( "and add (1) and (3)
\n" ); document.write( "(1) $\"+2x+%2B+2y+%2B+2z+=+16+\"$
\n" ); document.write( "(3) $\"+-2x+-+3y+%2B+3z+=+7+\"$
\n" ); document.write( "--------------------------
\n" ); document.write( " $\"+-y+%2B+5z+=+23+\"$
\n" ); document.write( "Subtract (2) from this result
\n" ); document.write( "---------------------------
\n" ); document.write( " $\"+-y+%2B+5z+=+23+\"$
\n" ); document.write( "(2) $\"+-3x+%2B+y+-+4z+=+-21+\"$
\n" ); document.write( "--------------------------
\n" ); document.write( " $\"+-3x+%2B+z+=+2+\"$
\n" ); document.write( "------------------
\n" ); document.write( "Now I can say:
\n" ); document.write( " $\"+y+=+5z+-+23+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+3x+=+z+-+2+\"$
\n" ); document.write( " $\"+x+=+%281%2F3%29%2Az+-+2%2F3+\"$
\n" ); document.write( "----------------------
\n" ); document.write( "Plug these results into (1)
\n" ); document.write( "(1) $\"+x+%2B+y+%2B+z+=+8+\"$
\n" ); document.write( "(1) $\"+%281%2F3%29%2Az+-+2%2F3+%2B+5z+-+23+%2B+z+=+8+\"$
\n" ); document.write( "(1) $\"+%2819%2F3%29%2Az+=+31+%2B+2%2F3+\"$
\n" ); document.write( "(1) $\"+19z+=+93+%2B+2+\"$
\n" ); document.write( "(1) $\"+z+=+95%2F19+\"$
\n" ); document.write( "(1) $\"+z+=+5+\"$
\n" ); document.write( "---------------------
\n" ); document.write( " $\"+-3x+%2B+z+=+2+\"$
\n" ); document.write( " $\"+-3x+%2B+5+=+2+\"$
\n" ); document.write( " $\"+-3x+=+-3+\"$
\n" ); document.write( " $\"+x+=+1+\"$
\n" ); document.write( "-------------------------
\n" ); document.write( " $\"+-y+%2B+5z+=+23+\"$
\n" ); document.write( " $\"+-y+%2B+5%2A5+=+23+\"$
\n" ); document.write( " $\"+-y+%2B+25+=+23+\"$
\n" ); document.write( " $\"+-y+=+-2+\"$
\n" ); document.write( " $\"+y+=+2+\"$
\n" ); document.write( "---------------
\n" ); document.write( "The solutions are:
\n" ); document.write( "x = 1
\n" ); document.write( "y = 2
\n" ); document.write( "z = 5
\n" ); document.write( "-----------------
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+x+%2B+y+%2B+z+=+8+\"$
\n" ); document.write( "(1) $\"+1+%2B+2+%2B+5+=+8+\"$
\n" ); document.write( "{1) $\"+8+=+8+\"$
\n" ); document.write( "OK
\n" ); document.write( "You can check (2) and (3)\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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