document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=184605>Question 184605</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For what values of c will the system have:\r<BR>\n" );
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document.write( "infinitely many solution<BR>\n" );
document.write( "1) 2x - 6y = c<BR>\n" );
document.write( "   6x - 18y = 30\r<BR>\n" );
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document.write( "2)no solution<BR>\n" );
document.write( "  x + 2y = 6<BR>\n" );
document.write( "  cx - 4y = 8\r<BR>\n" );
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document.write( "How do you do these questions? Can you explain how? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #138550 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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=138550\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> infinitely many solution<BR>\n" );
document.write( "1) 2x - 6y = c<BR>\n" );
document.write( "   6x - 18y = 30<BR>\n" );
document.write( "infinitely many solution means the two 'lines' are really the same line<BR>\n" );
document.write( "the second line above has two terms that are exactly 3 times the terms of the fisrt line (6x = 3*2x  and -18y = 3 *(-6y)) so if c is 3*30, then the two lines are really the same line.\r<BR>\n" );
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document.write( "2)no solution<BR>\n" );
document.write( "  x + 2y = 6<BR>\n" );
document.write( "  cx - 4y = 8\r<BR>\n" );
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document.write( "No solution occurs when the 'answer' is something that can't happen<BR>\n" );
document.write( "So let's double the first line to get<BR>\n" );
document.write( "2x + 4y = 12<BR>\n" );
document.write( "Now add the second line to it<BR>\n" );
document.write( "2x + 4y = 12<BR>\n" );
document.write( "cx -4y = 8<BR>\n" );
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document.write( "(2+c)x  = 20<BR>\n" );
document.write( "any c that that makes (2+x) a non-zero number will result in an x that 'works'. However, if c = -2, then we get<BR>\n" );
document.write( "(0*x) = 20<BR>\n" );
document.write( "0 times anything is 0, so that yields<BR>\n" );
document.write( "0 = 20\r<BR>\n" );
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document.write( "0=20 is impossible, so is c = -2 then ther eis no solution.,\r<BR>\n" );
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document.write( "make sense? </SPAN>\n" );
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