document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=849796>Question 849796</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have been trying to find a condition about r and s in this system that would make it inconsistent, but the -3rz keeps tripping me up!\r<BR>\n" );
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document.write( "here is the equation. \r<BR>\n" );
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document.write( "x - 2y + z = 2<BR>\n" );
document.write( "-x + 3y = 3 + s<BR>\n" );
document.write( "x - 5y - 3rz = 1  \r<BR>\n" );
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document.write( "thank you for helping!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #511803 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=511803\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Add eq.1 and 2 together,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2Bz=2%2B3%2Bs ALIGN=MIDDLE  ALT=\"y%2Bz=2%2B3%2Bs\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "4.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2Bz=5%2Bs ALIGN=MIDDLE  ALT=\"y%2Bz=5%2Bs\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Add eq. 2 and 3 together.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2y-3rz=3%2Bs%2B1 ALIGN=MIDDLE  ALT=\"-2y-3rz=3%2Bs%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "5.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2y-3rz=4%2Bs ALIGN=MIDDLE  ALT=\"-2y-3rz=4%2Bs\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Multiply eq. 1 by -2,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2y-2z=-2%285%2Bs%29 ALIGN=MIDDLE  ALT=\"-2y-2z=-2%285%2Bs%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "6.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2y-2z=-10-2s ALIGN=MIDDLE  ALT=\"-2y-2z=-10-2s\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Compare eq. 6 with eq. 5,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2y-3rz=4%2Bs ALIGN=MIDDLE  ALT=\"-2y-3rz=4%2Bs\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2z=-3rz ALIGN=MIDDLE  ALT=\"-2z=-3rz\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2=-3r ALIGN=MIDDLE  ALT=\"-2=-3r\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=2%2F3 ALIGN=MIDDLE  ALT=\"r=2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This makes the left hand side equal. <BR>\n" );
document.write( "So to be inconsistent, when the left hand sides are equal, the right hand sides are not equal. <BR>\n" );
document.write( "The two right hand sides are,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10-2s ALIGN=MIDDLE  ALT=\"-10-2s\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " and <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Bs ALIGN=MIDDLE  ALT=\"4%2Bs\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s ALIGN=MIDDLE  ALT=\"s\"   DISABLED_style= \"max-width:90%; height:auto;\" > when they are equal,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10-2s=4%2Bs ALIGN=MIDDLE  ALT=\"-10-2s=4%2Bs\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-14=3s ALIGN=MIDDLE  ALT=\"-14=3s\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=-14%2F4 ALIGN=MIDDLE  ALT=\"s=-14%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=2%2F3 ALIGN=MIDDLE  ALT=\"r=2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s ALIGN=MIDDLE  ALT=\"s\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equal to any number other than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2F3 ALIGN=MIDDLE  ALT=\"14%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the system is inconsistent.  </SPAN>\n" );
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