document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=59064>Question 59064</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve each of the following systems by addition. If a unique solution does not exist, state<BR>\n" );
document.write( "whether the system is inconsistent or dependent.\r<BR>\n" );
document.write( "\n" );
document.write( "2x+3y=1<BR>\n" );
document.write( "5x+3y=16<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x+5y=10<BR>\n" );
document.write( "-2x-10y= -20<BR>\n" );
document.write( "thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #40511 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=40511\">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<BR>\n" );
document.write( "whether the system is inconsistent or dependent.\r<BR>\n" );
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document.write( "L1) 2x+3y=1<BR>\n" );
document.write( "L2) 5x+3y=16<BR>\n" );
document.write( "Multiply  either L1 or L2 by -1 and add it to L1 and the y's will be eliminated and you can solve for x.  I'm going with L2:<BR>\n" );
document.write( "L2) -1(5x+3y)=-1(16) ---->> -5x-3y=-16<BR>\n" );
document.write( ":<BR>\n" );
document.write( "2x+3y=1<BR>\n" );
document.write( "-5x-3y=-16<BR>\n" );
document.write( "__________<BR>\n" );
document.write( "-3x=-15<BR>\n" );
document.write( "-3x/-3=-15/-3<BR>\n" );
document.write( "x=5<BR>\n" );
document.write( "Substitute that into either L1 or L2 and solve for y.  I'm going with L1:<BR>\n" );
document.write( "2(5)+3y=1<BR>\n" );
document.write( "10+3y=1<BR>\n" );
document.write( "-10+10+3y=-10+1<BR>\n" );
document.write( "3y=-9<BR>\n" );
document.write( "3y/3=-9/3<BR>\n" );
document.write( "y=-3<BR>\n" );
document.write( "The unique solution is: (5,-3)<BR>\n" );
document.write( ":::::::::::::::::::::::::::::::::<BR>\n" );
document.write( "and<BR>\n" );
document.write( "L1)x+5y=10<BR>\n" );
document.write( "L2)-2x-10y= -20<BR>\n" );
document.write( "Multiply L1 by 2 and add to L2 in an attempt to eliminate the x's.<BR>\n" );
document.write( "L1) 2(x+5y)=2(10)---->> 2x+10y=20<BR>\n" );
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( "There is no unique solution for this one. because 0 does = 0 this one is dependent.  It has an infinite number of solutions because graphically they are the same line and have all points in common.<BR>\n" );
document.write( "Happy Calculating!!! </SPAN>\n" );
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