document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=389307>Question 389307</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how many solutions exist?\r<BR>\n" );
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document.write( "1.<BR>\n" );
document.write( "3x-y=7<BR>\n" );
document.write( "6x-2y=6<BR>\n" );
document.write( "are the equations : consistent/inconsistent/dependent<BR>\n" );
document.write( "graphs of the lines are : intersect/parallel/coincide\r<BR>\n" );
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document.write( "2.<BR>\n" );
document.write( "3x+2y=5<BR>\n" );
document.write( "-x+5y=7<BR>\n" );
document.write( "are the equations : consistent/inconsistent/dependent<BR>\n" );
document.write( "graphs of the lines are : intersect/parallel/coincide\r<BR>\n" );
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document.write( "3.<BR>\n" );
document.write( "-x-2y=-3<BR>\n" );
document.write( "3x+6y=9<BR>\n" );
document.write( "are the equations : consistent/inconsistent/dependent<BR>\n" );
document.write( "graphs of the lines are : intersect/parallel/coincide<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #275870 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=275870\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.<BR>\n" );
document.write( "3x-y=7 ----> 6x - 2y = 14, after multiplying by 2.<BR>\n" );
document.write( "6x-2y=6<BR>\n" );
document.write( "The system is inconsistent.  The lines are parallel.\r<BR>\n" );
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document.write( "2. <BR>\n" );
document.write( "3x+2y=5<BR>\n" );
document.write( "-x+5y=7<BR>\n" );
document.write( "The system is consistent & independent.  (The determinant of the coefficient matrix is non-zero.)  The lines intersect.\r<BR>\n" );
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document.write( "3. <BR>\n" );
document.write( "-x-2y=-3 --------> 3x + 6y = 9, after multiplying both sides by -3<BR>\n" );
document.write( "3x+6y=9 (The two equations are the same!)<BR>\n" );
document.write( "The system is dependent.  The lines are coincident.<BR>\n" );
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