document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=886137>Question 886137</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help solving each system. Thank you.<BR>\n" );
document.write( "2x-y-z=1<BR>\n" );
document.write( "x+2y+z=0<BR>\n" );
document.write( "3x-y-2x=-1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #535703 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=535703\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Put into matrix form and use elementary row operations to convert into an upper triangular  arrangement.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C4%2C2%2C-1%2C-1%2C1%2C1%2C2%2C1%2C0%2C3%2C-1%2C-2%2C-1%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C4%2C2%2C-1%2C-1%2C1%2C1%2C2%2C1%2C0%2C3%2C-1%2C-2%2C-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C4%2C1%2C2%2C1%2C0%2C2%2C-1%2C-1%2C1%2C3%2C-1%2C-2%2C-1%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C4%2C1%2C2%2C1%2C0%2C2%2C-1%2C-1%2C1%2C3%2C-1%2C-2%2C-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C4%2C1%2C2%2C1%2C0%2C0%2C-5%2C-3%2C1%2C0%2C-7%2C-5%2C-1%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C4%2C1%2C2%2C1%2C0%2C0%2C-5%2C-3%2C1%2C0%2C-7%2C-5%2C-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, R2-2*R1, R3-3*R1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28matrix%283%2C4%2C1%2C2%2C1%2C0%2C0%2C5%2C3%2C1%2C0%2C7%2C5%2C1%29%29%29 ALIGN=MIDDLE  ALT=\"%28%28matrix%283%2C4%2C1%2C2%2C1%2C0%2C0%2C5%2C3%2C1%2C0%2C7%2C5%2C1%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, multiply row 2 and 3 by -1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28matrix%283%2C4%2C1%2C2%2C1%2C0%2C0%2C35%2C21%2C7%2C0%2C35%2C25%2C5%29%29%29 ALIGN=MIDDLE  ALT=\"%28%28matrix%283%2C4%2C1%2C2%2C1%2C0%2C0%2C35%2C21%2C7%2C0%2C35%2C25%2C5%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, 7*R2, 5*R3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C4%2C1%2C2%2C1%2C0%2C0%2C5%2C3%2C1%2C0%2C0%2C2%2C1%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C4%2C1%2C2%2C1%2C0%2C0%2C5%2C3%2C1%2C0%2C0%2C2%2C1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, (1/7)R2, (1/2)R3\r<BR>\n" );
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document.write( "This can continue using subtraction to eliminate elements above the diagonal.  This is already in a form that says, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=-1%2F2 ALIGN=MIDDLE  ALT=\"z=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and you can use this to back substitute and solve for the next variables one at a time.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C4%2C1%2C2%2C1%2C0%2C0%2C5%2C3%2C1%2C0%2C0%2C1%2C-1%2F2%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C4%2C1%2C2%2C1%2C0%2C0%2C5%2C3%2C1%2C0%2C0%2C1%2C-1%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, R3 divid by 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C4%2C1%2C2%2C0%2C1%2F2%2C0%2C5%2C0%2C5%2F2%2C0%2C0%2C1%2C-1%2F2%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C4%2C1%2C2%2C0%2C1%2F2%2C0%2C5%2C0%2C5%2F2%2C0%2C0%2C1%2C-1%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, R2-3R3, R1-R3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C4%2C1%2C2%2C0%2C1%2F2%2C0%2C1%2C0%2C1%2F2%2C0%2C0%2C1%2C-1%2F2%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C4%2C1%2C2%2C0%2C1%2F2%2C0%2C1%2C0%2C1%2F2%2C0%2C0%2C1%2C-1%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, Divide R2 by 5\r<BR>\n" );
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document.write( "And next do R1-2*R2, ...  and your matrix tells you the solution.\r<BR>\n" );
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document.write( "After so much long, detailed work, I believe I see a mistake...<BR>\n" );
document.write( "hopefully you can understand the process being shown and can check and reduce the matrix on paper and be sure of the correct answers.\r<BR>\n" );
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document.write( "REDONE ON PAPER:<BR>\n" );
document.write( "Tracing the work between paper and the (wrongly) posted solution is difficult.  Let me just post here my redone RESULT solution matrix; likely some of the arithmetic computation was wrong in computing one of the elements.<BR>\n" );
document.write( "This one should be right...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C4%2C1%2C0%2C0%2C2%2F11%2C0%2C1%2C-5%2F11%2C0%2C0%2C1%2C12%2F11%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C4%2C1%2C0%2C0%2C2%2F11%2C0%2C1%2C-5%2F11%2C0%2C0%2C1%2C12%2F11%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Rendering is failing at the moment.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-7%2F11 ALIGN=MIDDLE  ALT=\"y=-7%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=12%2F11 ALIGN=MIDDLE  ALT=\"z=12%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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