document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=679648>Question 679648</A>: <I><SPAN STYLE=\"word-break: break-all;\"> need help solving linear equation in three variables using the elimination method.<BR>\n" );
document.write( "-3x-2y+4z=-5<BR>\n" );
document.write( "2x+5y-3z=3<BR>\n" );
document.write( "4x-y+7z=15\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #422033 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=422033\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> They are trying to torment you here, the solutions are not integers!\r<BR>\n" );
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document.write( "-3x  -2y + 4z =-5<BR>\n" );
document.write( " 2x + 5y - 3z = 3<BR>\n" );
document.write( " 4x - y + 7z = 15 <BR>\n" );
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document.write( "Multiply the 1st equation by -1 and add<BR>\n" );
document.write( "3x  + 2y - 4z = 5<BR>\n" );
document.write( " 2x + 5y - 3z = 3<BR>\n" );
document.write( " 4x - y + 7z = 15 <BR>\n" );
document.write( "--------------------adding eliminates z<BR>\n" );
document.write( "9x + 6y = 23<BR>\n" );
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document.write( "use the first two original equations, mult the 1st by 3, the 2nd by 4<BR>\n" );
document.write( "-9x - 6y + 12z = -15<BR>\n" );
document.write( " 8x + 20y -12z = 12<BR>\n" );
document.write( "--------------------adding eliminates z<BR>\n" );
document.write( "-x + 14y = -3<BR>\n" );
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document.write( "the above equation by 9, add to the 1st \"two unknown\" equation<BR>\n" );
document.write( "-9x + 126y = -27<BR>\n" );
document.write( " 9x +  6y = 23<BR>\n" );
document.write( "------------------adding eliminates x find y<BR>\n" );
document.write( " 132y = -4<BR>\n" );
document.write( "y = 4/132 = -1/33, -.0303 as a decimal<BR>\n" );
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document.write( "Find x using 9x + 6y = 23<BR>\n" );
document.write( "9x + 6(-1/33) = 23<BR>\n" );
document.write( "9x + (-6/33) = 23<BR>\n" );
document.write( "9x + (-2/11) = 23<BR>\n" );
document.write( "9x = 23 + 2/11<BR>\n" );
document.write( "9x = 253/11 + 2/11<BR>\n" );
document.write( "9x = 255/11<BR>\n" );
document.write( "x = 1/9 * 251/11 = 255/99, 2.576 as a decimal<BR>\n" );
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document.write( "Find z using 4x - y + 7z = 15, <BR>\n" );
document.write( "use decimals, here, avoid these disgusting fractions<BR>\n" );
document.write( "4(2.576) - (-.0303) + 7z = 15<BR>\n" );
document.write( "10.303 + .0303 + 7z = 15<BR>\n" );
document.write( "10.333 + 7z = 15<BR>\n" );
document.write( "7z = 15 - 10.333<BR>\n" );
document.write( "7z = 4.667<BR>\n" );
document.write( "z = 4.667/7 <BR>\n" );
document.write( "z = .6666, which is 2/3 if you insist on fractions<BR>\n" );
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document.write( "Summarize this mess: x = 2.576, y = -.0303, z = .667<BR>\n" );
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document.write( "You can confirm this in the original equations, if you are totally bored with life.\r<BR>\n" );
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