document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=105394>Question 105394</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve each of the following systems 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( " 2x + 3y = 1  <BR>\n" );
document.write( "and 5x + 3y =16 \r<BR>\n" );
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document.write( "x+5y = 10 <BR>\n" );
document.write( "and -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 #76772 by </B><A HREF=/tutors/aboutme.mpl?userid=elima><B>elima(1433)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=elima><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=76772\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve each of the following systems 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( "2x + 3y = 1  <BR>\n" );
document.write( "and 5x + 3y =16 \r<BR>\n" );
document.write( "\n" );
document.write( "x+ 5y = 10 <BR>\n" );
document.write( "and -2x – 10y = -20<BR>\n" );
document.write( "=================================<BR>\n" );
document.write( "2x+3y=1<BR>\n" );
document.write( "5x+3y=16<BR>\n" );
document.write( "Multiply the first equation by -1;<BR>\n" );
document.write( "(-1)2x+3y =1<BR>\n" );
document.write( "-2x-3y=-1<BR>\n" );
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document.write( "now add the equations;<BR>\n" );
document.write( "-2x-3y=-1<BR>\n" );
document.write( "5x+3y=16<BR>\n" );
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document.write( "3x=15<BR>\n" );
document.write( "x=5<BR>\n" );
document.write( "==============<BR>\n" );
document.write( "2(5)+3y=1<BR>\n" );
document.write( "10+3y=1<BR>\n" );
document.write( "3y=-9<BR>\n" );
document.write( "y=-3<BR>\n" );
document.write( "So this equation has a solution, it is independent<BR>\n" );
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document.write( "x+5y = 10 <BR>\n" );
document.write( "-2x – 10y = -20<BR>\n" );
document.write( "=====================<BR>\n" );
document.write( "lets multiply the first equation by 2;<BR>\n" );
document.write( "(2)x+5y=10<BR>\n" );
document.write( "2x+10y=20<BR>\n" );
document.write( "===============<BR>\n" );
document.write( "Now add the equations;<BR>\n" );
document.write( "2x+10y=20<BR>\n" );
document.write( "-2x=10y=-20<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "0=0<BR>\n" );
document.write( "dependent<BR>\n" );
document.write( ":)\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );