document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=41946>Question 41946</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following system by addition. If a unique solution does not exist, state whether the system is inconsistent or dependent.\r<BR>\n" );
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document.write( "x+5y=10<BR>\n" );
document.write( "-2x-10y=-20 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #27135 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=27135\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Consider the second equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x-10y=-20 ALIGN=MIDDLE  ALT=\"-2x-10y=-20\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "This can be simplified into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B10y=20 ALIGN=MIDDLE  ALT=\"2x%2B10y=20\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5y=10 ALIGN=MIDDLE  ALT=\"x%2B5y=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Thus the second equation is identical with the first one.<BR>\n" );
document.write( "So the system is dependent.\r<BR>\n" );
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document.write( "So, ultimately, we are left with only one equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5y=10 ALIGN=MIDDLE  ALT=\"x%2B5y=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > but 2 unknowns.<BR>\n" );
document.write( "To determine 2 unknowns we need two different equations; otherwise from one equation we cannot find a unique solution. </SPAN>\n" );
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