document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=187294>Question 187294</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the linear system with a single solution or using the addtion and substitution method. \r<BR>\n" );
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document.write( "14)2x-y+3z=14<BR>\n" );
document.write( "    x+y-2z=-5<BR>\n" );
document.write( "   3x+y- z=2 \r<BR>\n" );
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document.write( "18) x-3y+2z=-11<BR>\n" );
document.write( "   2x-4y+3z=-15<BR>\n" );
document.write( "   3x-5y-4z=5''.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #140391 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=140391\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve each system in three variables <BR>\n" );
document.write( "14)<BR>\n" );
document.write( "2x-y+3z=14<BR>\n" );
document.write( "x+y-2z=-5<BR>\n" );
document.write( "3x+y- z=2 <BR>\n" );
document.write( "------------<BR>\n" );
document.write( "Elimination and substitution is one way to do these.<BR>\n" );
document.write( "1st, pick a variable to eliminate from 2 of the eqns.  Since y has a coeff of 1 in all 3, it's the easiest.<BR>\n" );
document.write( "Add eqn 3 to eqn 1, and then subtract it from eqn 2.<BR>\n" );
document.write( "2x-y+3z=14<BR>\n" );
document.write( "3x+y- z=2 <BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "5x+0y+2z = 16  Eqn A<BR>\n" );
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document.write( "x+y-2z=-5<BR>\n" );
document.write( "3x+y- z=2 <BR>\n" );
document.write( "----------<BR>\n" );
document.write( "-2x+0y-z = -7 Eqn B<BR>\n" );
document.write( "Now there are 2 eqns in x and z<BR>\n" );
document.write( "Multiply Eqn A and B by something to get the same coeff for either x or z.<BR>\n" );
document.write( "Multiply B by 2 to get 2z in both<BR>\n" );
document.write( "5x+0y+2z = 16  Eqn A<BR>\n" );
document.write( "-4x-2z = -14  Eqn B times 2<BR>\n" );
document.write( "------------- Add these<BR>\n" );
document.write( "x = 2<BR>\n" );
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document.write( "Sub x into Eqn A, find z<BR>\n" );
document.write( "z = 3<BR>\n" );
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document.write( "Sub z and z into any eqn to find y<BR>\n" );
document.write( "y = -2<BR>\n" );
document.write( "------<BR>\n" );
document.write( "x = 2<BR>\n" );
document.write( "y = -1<BR>\n" );
document.write( "z = 3<BR>\n" );
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document.write( "Try this one.  email me via the thank you note for help, or to check you work.<BR>\n" );
document.write( "18) <BR>\n" );
document.write( "x-3y+2z=-11<BR>\n" );
document.write( "2x-4y+3z=-15<BR>\n" );
document.write( "3x-5y-4z=5 </SPAN>\n" );
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