document.write( "Question 907725: Please help without using the matrix system! thank you
\n" ); document.write( "x+y+z-w=5
\n" ); document.write( "2x+y-z+w=6
\n" ); document.write( "x-5y+3z+w=9
\n" ); document.write( "-x-y+z+4w=7
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Algebra.Com's Answer #550564 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
OK so use row operations and elimination to reduce your variables.
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\n" ); document.write( " $\"R%5B1%5D\"$ : $\"x%2By%2Bz-w=5\"$
\n" ); document.write( " $\"R%5B2%5D\"$ : $\"2x%2By-z%2Bw=6\"$
\n" ); document.write( " $\"R%5B3%5D\"$ : $\"x-5y%2B3z%2Bw=9\"$
\n" ); document.write( " $\"R%5B4%5D\"$ : $\"-x-y%2Bz%2B4w=7\"$
\n" ); document.write( "Let's get rid of $\"w\"$ first.
\n" ); document.write( " $\"R%5B5%5D=R%5B1%5D%2BR%5B2%5D\"$ : $\"x%2By%2Bz-w%2B2x%2By-z%2Bw=5%2B6\"$
\n" ); document.write( " $\"R%5B5%5D=R%5B1%5D%2BR%5B2%5D\"$ : $\"3x%2B2y=11\"$
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\n" ); document.write( " $\"R%5B6%5D=R%5B1%5D%2BR%5B3%5D\"$ : $\"x%2By%2Bz-w%2Bx-5y%2B3z%2Bw=5%2B9\"$
\n" ); document.write( " $\"R%5B6%5D=R%5B1%5D%2BR%5B3%5D\"$ : $\"2x-4y%2B4z=14\"$
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\n" ); document.write( " $\"R%5B7%5D=4%2AR%5B1%5D%2BR%5B4%5D\"$ : $\"4x%2B4y%2B4z-4w-x-y%2Bz%2B4w=20%2B7\"$
\n" ); document.write( " $\"R%5B7%5D=4%2AR%5B1%5D%2BR%5B4%5D\"$ : $\"3x%2B3y%2B5z=27\"$
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\n" ); document.write( "OK, $\"R%5B5%5D\"$ already has $\"z\"$ eliminated, so let's pair up $\"R%5B6%5D\"$ and $\"R%5B7%5D\"$ to do the same.
\n" ); document.write( " $\"R%5B8%5D=5%2AR%5B6%5D-4%2AR%5B7%5D\"$ : $\"10x-20y%2B20z-12x-12y-20z=70-108\"$
\n" ); document.write( " $\"R%5B8%5D=5%2AR%5B6%5D-4%2AR%5B7%5D\"$ : $\"-2x-32y=-38\"$
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\n" ); document.write( "Finally, multiply $\"R%5B5%5D\"$ by $\"16\"$ and add to $\"R%5B8%5D\"$ to eliminate $\"y\"$ .
\n" ); document.write( " $\"R%5B9%5D=16%2AR5%2BR8\"$ : $\"48x%2B32y-2x-32y=176-38\"$
\n" ); document.write( " $\"R%5B9%5D=16%2AR5%2BR8\"$ : $\"46x=148\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"x=148%2F46\"$
\n" ); document.write( " $\"x=3\"$
\n" ); document.write( "Then work backwards,
\n" ); document.write( " $\"R%5B5%5D\"$ : $\"3%283%29%2B2y=11\"$
\n" ); document.write( " $\"2y=2\"$
\n" ); document.write( " $\"y=1\"$
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\n" ); document.write( " $\"R%5B6%5D\"$ : $\"2%283%29-4%281%29%2B4z=14\"$
\n" ); document.write( " $\"6-4%2B4z=14\"$
\n" ); document.write( " $\"4z=12\"$
\n" ); document.write( " $\"z=3\"$
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\n" ); document.write( " $\"R%5B1%5D\"$ : $\"3%2B1%2B3-w=5\"$
\n" ); document.write( " $\"w=2\"$ \r
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