document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=12428>Question 12428</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me solve this problem.<BR>\n" );
document.write( "Solve the system using any algebraic method\r<BR>\n" );
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document.write( "x + y + 2z =5 <BR>\n" );
document.write( "x + 2y + z = 8 <BR>\n" );
document.write( "2x + 3y - z = 1\r<BR>\n" );
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document.write( "                   Thanks for helping me solve this problem.<BR>\n" );
document.write( "                                                    KAt  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #6329 by </B><A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><B>AnlytcPhil(1806)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=AnlytcPhil><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=6329\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face = \"courier new\" size = 3 color = \"blue\"><b><BR>\n" );
document.write( "`x +` y + 2z = 5 <BR>\n" );
document.write( "`x + 2y +` z = 8 <BR>\n" );
document.write( "2x + 3y -` z = 1<BR>\n" );
document.write( "`<BR>\n" );
document.write( "One way is to eliminate the three lower left terms,<BR>\n" );
document.write( "the ones I have colored red:<BR>\n" );
document.write( "`<BR>\n" );
document.write( "`x +` y + 2z = 5 <BR>\n" );
document.write( "`<font color = \"red\"><b>x</font></b> + 2y +` z = 8 <BR>\n" );
document.write( "<font color = \"red\"><b>2x + 3y</font></b> -` z = 1<BR>\n" );
document.write( "`<BR>\n" );
document.write( "Instead of solving yours, I'll solve one just like it, OK?<BR>\n" );
document.write( "Then you can use it as a model to solve yours.<BR>\n" );
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document.write( "`x - 3y + 4z =` 45 <BR>\n" );
document.write( "3x + 2y - 5z = -21 <BR>\n" );
document.write( "4x + 5y - 3z = -32<BR>\n" );
document.write( "`<BR>\n" );
document.write( "`x - 3y + 4z = `45 <BR>\n" );
document.write( "<font color = \"red\"><b>3x</font></b> + 2y - 5z = -21 <BR>\n" );
document.write( "<font color = \"red\"><b>4x + 5y</font></b> - 3z = -32<BR>\n" );
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document.write( "To get rid of the 3x, multiply the top equation by -3<BR>\n" );
document.write( "and add it to 1 times the middle equation, but restore the<BR>\n" );
document.write( "top equation:<BR>\n" );
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document.write( "-3[ x - 3y + 4z =` 45] <BR>\n" );
document.write( "`1[3x + 2y - 5z = -21] <BR>\n" );
document.write( "` `4x + 5y - 3z = -32<BR>\n" );
document.write( "`<BR>\n" );
document.write( "`x - 3y +` 4z = ` 45 <BR>\n" );
document.write( "` ` 11y - 17z = -156 <BR>\n" );
document.write( "4x + 5y -` 3z =` -32<BR>\n" );
document.write( "`<BR>\n" );
document.write( "To get rid of the 4x, multiply the top equation by -4<BR>\n" );
document.write( "and add it to 1 times the bottom equation, but again<BR>\n" );
document.write( "restore the top equation:<BR>\n" );
document.write( "`<BR>\n" );
document.write( "-4[ x - 3y +` 4z = ` 45]<BR>\n" );
document.write( "` ` ` `11y - 17z = -156 <BR>\n" );
document.write( "`1[4x + 5y - `3z = `-32]<BR>\n" );
document.write( "`<BR>\n" );
document.write( "x - 3y + `4z = ` 45 <BR>\n" );
document.write( "` `11y - 17z = -156<BR>\n" );
document.write( "` `17y - 19z = -212<BR>\n" );
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document.write( "To get rid of the last one, 17y, multiply the middle equation by -17 and add it to 11 times the bottom equation, but<BR>\n" );
document.write( "restore the middle equation:<BR>\n" );
document.write( "`<BR>\n" );
document.write( "` ` x - 3y +  4z = ` 45 <BR>\n" );
document.write( "-17[ ` 11y - 17z = -156<BR>\n" );
document.write( "`11[ ` 17y - 19z = -212<BR>\n" );
document.write( "`<BR>\n" );
document.write( "x - 3y + `4z = ` 45 <BR>\n" );
document.write( "`` 11y - 17z = -156<BR>\n" );
document.write( "` ` ` ` `80z =  320<BR>\n" );
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document.write( "Now that those three bottom left terms have been<BR>\n" );
document.write( "eliminated, solve the bottom equation:<BR>\n" );
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document.write( "` ` ` ` `80z = 320<BR>\n" );
document.write( "` ` ` ` ` `z = 4<BR>\n" );
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document.write( "Substitute z=4 into the middle equation and solve<BR>\n" );
document.write( "for y<BR>\n" );
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document.write( "`11y - 17(4) = -156<BR>\n" );
document.write( "` ` 11y - 68 = -156<BR>\n" );
document.write( "` ` ` ` `11y = -88<BR>\n" );
document.write( "` ` ` ` ` `y = -8<BR>\n" );
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document.write( "Fimally substitute z=4 and y=-8 into the top equation and solve for x:<BR>\n" );
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document.write( "x - 3(-8) + 4(4) = 45<BR>\n" );
document.write( "` ` `x + 24 + 16 = 45<BR>\n" );
document.write( "` ` ` ` ` x + 40 = 45<BR>\n" );
document.write( "` ` ` ` ` ` ` `x = 5<BR>\n" );
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document.write( "So the solution is (x, y, z) = (5, -8, 4)<BR>\n" );
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document.write( "Now use this as a model to solve yours by.  The solution is<BR>\n" );
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document.write( "(x, y, z) = (-7, 6, 3) <BR>\n" );
document.write( "Edwin</b></font><BR>\n" );
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