document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1114851>Question 1114851</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Subscript notation is frequently used for working with larger systems of equations. Use a matrix approach to solve the system. Express the solutions as 4-tuples of the form <BR>\n" );
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document.write( "x1 + 3x2 &#8722; x3 + 2x4	 = 	&#8722;15<BR>\n" );
document.write( "2x1 + 7x2 + 2x3 &#8722; x4	 = 	27<BR>\n" );
document.write( "&#8722;3x1 &#8722; 8x2 + 3x3 + x4	 = 	&#8722;10<BR>\n" );
document.write( "4x1 + 11x2 &#8722; 2x3 &#8722; 3x4	 = 	35\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 #729779 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=729779\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your matrix:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%284%2C5%2C1%2C%093%2C%09-1%2C%092%2C%09-15%2C%0D%0A2%2C%097%2C%092%2C%09-4%2C%0927%2C%0D%0A-3%2C%09-8%2C%093%2C%094%2C%09-10%2C%0D%0A4%2C%0911%2C%09-2%2C%09-3%2C%0935%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Find the pivot in the 1st column in the 1st row:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%284%2C5%2C%0D%0Ahighlight%281%29%2C%093%2C%09-1%2C%092%2C%09-15%2C%0D%0A2%2C%097%2C%092%2C%09-4%2C%0927%2C%0D%0A-3%2C%09-8%2C%093%2C%094%2C%09-10%2C%0D%0A4%2C%0911%2C%09-2%2C%09-3%2C%0935%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Eliminate the 1st column:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%284%2C5%2C%0D%0A1%2C%093%2C%09-1%2C%092%2C%09-15%2C%0D%0A0%2C%091%2C%094%2C%09-8%2C%0957%2C%0D%0A0%2C%091%2C%090%2C%0910%2C%09-55%2C%0D%0A0%2C%09-1%2C%092%2C%09-11%2C%0995%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Find the pivot in the 2nd column in the 2nd row:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%284%2C5%2C%0D%0A1%2C%093%2C%09-1%2C%092%2C%09-15%2C%0D%0A0%2C%09highlight%281%29%2C%094%2C%09-8%2C%0957%2C%0D%0A0%2C%091%2C%090%2C%0910%2C%09-55%2C%0D%0A0%2C%09-1%2C%092%2C%09-11%2C%0995%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Eliminate the 2nd column:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%284%2C5%2C%0D%0A1%2C%090%2C%09-13%2C%0926%2C%09-186%2C%0D%0A0%2C%091%2C%094%2C%09-8%2C%0957%2C%0D%0A0%2C%090%2C%09-4%2C%0918%2C%09-112%2C%0D%0A0%2C%090%2C%096%2C%09-19%2C%09152%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Make the pivot in the 3rd column by dividing the 3rd row by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   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=matrix%284%2C5%2C%0D%0A1%2C%090%2C%09-13%2C%0926%2C%09-186%2C%0D%0A0%2C%091%2C%094%2C%09-8%2C%0957%2C%0D%0A0%2C%090%2C%091%2C%09-9%2F2%2C%0928%2C%0D%0A0%2C%090%2C%096%2C%09-19%2C%09152%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Eliminate the 3rd column:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%284%2C5%2C%0D%0A1%2C%090%2C%090%2C%09-65%2F2%2C%09178%2C%0D%0A0%2C%091%2C%090%2C%0910%2C%09-55%2C%0D%0A0%2C%090%2C%091%2C%09-9%2F2%2C%0928%2C%0D%0A0%2C%090%2C%090%2C%098%2C%09-16%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Make the pivot in the 4th column by dividing the 4th row by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   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=matrix%284%2C5%2C%0D%0A1%2C%090%2C%090%2C%09-65%2F2%2C%09178%2C%0D%0A0%2C%091%2C%090%2C%0910%2C%09-55%2C%0D%0A0%2C%090%2C%091%2C%09-9%2F2%2C%0928%2C%0D%0A0%2C%090%2C%090%2C%091%2C%09-2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Eliminate the 4th column:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%284%2C5%2C%0D%0A1%2C%090%2C%090%2C%090%2C%09113%2C%0D%0A0%2C%091%2C%090%2C%090%2C%09-35%2C%0D%0A0%2C%090%2C%091%2C%090%2C%0919%2C%0D%0A0%2C%090%2C%090%2C%091%2C%09-2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solution set:\r<BR>\n" );
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document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=113 ALIGN=MIDDLE  ALT=\"113\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-35 ALIGN=MIDDLE  ALT=\"+-35\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19 ALIGN=MIDDLE  ALT=\"19\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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