document.write( "Question 118587: solve for z\r
\n" ); document.write( "\n" ); document.write( "3x + 4y + z = 11.5
\n" ); document.write( "2x - 2y - 3z = 1.5
\n" ); document.write( "4x + y - 2z = 12.5\r
\n" ); document.write( "\n" ); document.write( "(a) .5
\n" ); document.write( "(b) .2
\n" ); document.write( "(c) 5
\n" ); document.write( "(d) 1.5 \n" ); document.write( "

Algebra.Com's Answer #86801 by MathLover1(20849) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"3x+%2B+4y+%2B+z+=+11.5\"$ ЕЕЕЕЕЕЕЕ..(1)
\n" ); document.write( " $\"2x+-+2y+-+3z+=+1.5\"$ ЕЕЕЕЕЕЕЕЕ(2)
\n" ); document.write( " $\"4x+%2B+y+-+2z+=+12.5\"$ ЕЕЕЕЕЕЕЕЕ(3) \r
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\n" ); document.write( "\n" ); document.write( "Take (1) and (2), and eliminate $\"y\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"3x+%2B+4y+%2B+z+=+11.5\"$ ЕЕЕЕЕЕЕЕ..(1)
\n" ); document.write( " $\"2x+-+2y+-+3z+=+1.5\"$ ЕЕЕЕЕЕЕЕЕ(2)Е->Е.multiply by $\"2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"3x+%2B+4y+%2B+z+=+11.5\"$
\n" ); document.write( "+ $\"4x+-+4y+-+6z+=+3\"$ ЕЕЕЕ.add them
\n" ); document.write( "--------------------------------\r
\n" ); document.write( "\n" ); document.write( " $\"7x+-+5y+=+14.5\"$ ЕЕЕЕЕЕЕЕЕ(a)\r
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\n" ); document.write( "\n" ); document.write( "Now take (2) and (3), and eliminate $\"y\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"2x+-+2y+-+3z+=+1.5\"$
\n" ); document.write( " $\"4x+%2B+y+-+2z+=+12.5\"$ ЕЕЕЕЕЕЕ->Е multiply by $\"2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"2x+-+2y+-+3z+=+1.5\"$
\n" ); document.write( "+ $\"8x+%2B+2y+-+4z+=+25\"$ ЕЕЕЕЕЕ.. add them
\n" ); document.write( "-----------------------------\r
\n" ); document.write( "\n" ); document.write( " $\"10x+-+7z+=+26.5\"$ ЕЕЕЕЕЕЕЕЕ(b)\r
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\n" ); document.write( "\n" ); document.write( "Now take (a) and (b) and eliminate $\"x\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"7x+-+5y+=+14.5\"$ ЕЕЕЕЕЕЕ->ЕЕmultiply by $\"-10\"$
\n" ); document.write( " $\"10x+-+7z+=+26.5\"$ ЕЕЕЕЕЕЕ->ЕЕmultiply by $\"7\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"-70x+%2B+50z+=+-145\"$ ЕЕЕ..
\n" ); document.write( " $\"70x+-+49z+=+185.5\"$ ЕЕЕ.. ЕЕЕЕ.. add them
\n" ); document.write( "---------------------------
\n" ); document.write( " $\"z+=+-145+%2B+185.5\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"z+=+40.5\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now find $\"x\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"7x+-+5y+=+14.5\"$ ЕЕЕЕЕЕЕЕЕ(a)\r
\n" ); document.write( "\n" ); document.write( " $\"7x++=+5z+%2B+14.5\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"7x++=+5%2840.5%29+%2B+14.5\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"7x++=+202.5+%2B+14.5\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"7x++=+217\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x++=+31\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now find $\"y\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"2x+-+2y+-+3z+=+1.5\"$ ЕЕЕЕЕЕЕЕЕ(2)ЕЕ.\r
\n" ); document.write( "\n" ); document.write( " $\"-2y++=+-2x+%2B+3z+%2B1.5\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-2y++=+-2%2831%29+%2B+3%2840.5%29+%2B1.5\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-2y++=+-62+%2B+121.5+%2B1.5\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-2y++=+-62+%2B+123\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-2y++=+61\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y++=+61%2F-2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y++=+-30.5\"$ \r
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\n" ); document.write( "\n" ); document.write( "Check:\r
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\n" ); document.write( "\n" ); document.write( " $\"x++=+31\"$
\n" ); document.write( " $\"y++=+-30.5\"$
\n" ); document.write( " $\"z+=+40.5\"$ \r
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\n" ); document.write( "\n" ); document.write( "Plug in values in original equations:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"3x+%2B+4y+%2B+z+=+11.5\"$ ЕЕЕЕЕЕЕЕ..(1)\r
\n" ); document.write( "\n" ); document.write( " $\"3%2831%29+%2B+4%28-30.5%29+%2B+40.5+=+11.5\"$ Е\r
\n" ); document.write( "\n" ); document.write( " $\"93+-122+%2B+40.5+=+11.5\"$ Е\r
\n" ); document.write( "\n" ); document.write( " $\"133.5+-122++=+11.5\"$ Е\r
\n" ); document.write( "\n" ); document.write( " $\"11.5+=+11.5\"$ Е\r
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\n" ); document.write( "\n" ); document.write( " $\"2x+-+2y+-+3z+=+1.5\"$ ЕЕЕЕЕЕЕЕЕ(2)\r
\n" ); document.write( "\n" ); document.write( " $\"2%2831%29+-+2%28-30.5%29+-+3%2840.5+%29+=+1.5\"$ ЕЕ\r
\n" ); document.write( "\n" ); document.write( " $\"62+%2B+61+-+121.5+=+1.5\"$ ЕЕ\r
\n" ); document.write( "\n" ); document.write( " $\"123-+121.5+=+1.5\"$ ЕЕ\r
\n" ); document.write( "\n" ); document.write( " $\"1.5++=+1.5\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"4x+%2B+y+-+2z+=+12.5\"$ ЕЕЕЕЕЕЕЕЕ(3) \r
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\n" ); document.write( "\n" ); document.write( " $\"4%2831%29+-30.5++-+2%2840.5+%29++=+12.5\"$ ) \r
\n" ); document.write( "\n" ); document.write( " $\"124+-30.5++-+81++=+12.5\"$ ) \r
\n" ); document.write( "\n" ); document.write( " $\"124+-111.5+++=+12.5\"$ )\r
\n" ); document.write( "\n" ); document.write( " $\"12.5+++=+12.5\"$ )\r
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