document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=353410>Question 353410</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the system of linear equations in trian-<BR>\n" );
document.write( "gular form<BR>\n" );
document.write( "x + y + z = 7<BR>\n" );
document.write( "3x + 4y + z = 13<BR>\n" );
document.write( "2x &#8722; 2y + 9z = 7<BR>\n" );
document.write( "What is triangular form and how would I solve this problem using it? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #252510 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=252510\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x + y + z = 7<BR>\n" );
document.write( "3x + 4y + z = 13<BR>\n" );
document.write( "2x &#8722; 2y + 9z = 7<BR>\n" );
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document.write( "Subtract 3 times the 1st line from the 2nd line<BR>\n" );
document.write( "Subtract 2 times the 1st line from the 3rd line<BR>\n" );
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document.write( "x + y + z = 7<BR>\n" );
document.write( "0 + y - 2z = -8<BR>\n" );
document.write( "0 -4y + 7z = -7<BR>\n" );
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document.write( "Add 4 times the 2nd line to the 3rd to get:<BR>\n" );
document.write( "x + y + z = 7<BR>\n" );
document.write( "0 + y - 2z = -8<BR>\n" );
document.write( "0 + 0 - z = -39<BR>\n" );
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document.write( "That is the triangle form (see the triangle of zeros in<BR>\n" );
document.write( "the left bottom corner.<BR>\n" );
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document.write( "Note that you can solve for \"z\" in the 3rd line z = 39<BR>\n" );
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document.write( "Then you can substiute 39 for \"z\" in the 2nd line and solve for y = 70.<BR>\n" );
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document.write( "Then you can substitute for z and for y in the 1st line and solve for x=-102.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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