document.write( "Question 902201: Need help solving systems in three variable - x+y+z=57,-2x+y+=3,x-z=6 \n" ); document.write( "

Algebra.Com's Answer #547208 by Fombitz(32388) $\"\"$ $\"About$

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From eq. 3,
\n" ); document.write( " $\"x-z=6\"$
\n" ); document.write( " $\"z=x-6\"$
\n" ); document.write( "Substitute into eq. 1,
\n" ); document.write( " $\"x%2By%2B%28x-6%29=57\"$
\n" ); document.write( " $\"2x%2By=63\"$
\n" ); document.write( "Then from eq. 2,
\n" ); document.write( " $\"y=3%2B2x\"$
\n" ); document.write( "Substituting,
\n" ); document.write( " $\"2x%2B%283%2B2x%29=63\"$
\n" ); document.write( " $\"4x=60\"$
\n" ); document.write( " $\"x=15\"$
\n" ); document.write( "Now working backwards,
\n" ); document.write( " $\"y=3%2B2%2815%29\"$
\n" ); document.write( " $\"y=3%2B30\"$
\n" ); document.write( " $\"y=33\"$
\n" ); document.write( "and finally,
\n" ); document.write( " $\"z=15-6\"$
\n" ); document.write( " $\"z=9\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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