document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=63064>Question 63064</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0072549017/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following systems by addition. If a unique solution does not exist, state whether the system is inconsistent or dependent.<BR>\n" );
document.write( "x + 5y = 10<BR>\n" );
document.write( "-2x - 10y = -20<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #43895 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=43895\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve the following systems by addition. If a unique solution does not exist, state whether the system is inconsistent or dependent.<BR>\n" );
document.write( "E1:  x + 5y = 10<BR>\n" );
document.write( "E2:  -2x - 10y = -20<BR>\n" );
document.write( "Multiply E1 by 2 and add it to E2.<BR>\n" );
document.write( "E1:  2(x+5y)=2(10) --> 2x+10y=20<BR>\n" );
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document.write( "2x+10y=20<BR>\n" );
document.write( "-2x-10y=-20<BR>\n" );
document.write( "____________<BR>\n" );
document.write( "0+0=0<BR>\n" );
document.write( "0=0<BR>\n" );
document.write( "When all your variables are eliminated, you have one of two cases, 0=0 means that the system is dependent.  The lines are lying right on top of each other and there are infinitely many solutions because they have all points in common.<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "If both your variables are eliminated and your left with 0=(something other than 0).  Then you would have had an inconsitent system.  The lines would be parallel and never intersect, thus giving no solution.<BR>\n" );
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document.write( "Happy Calculating!!!<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );