document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1019644>Question 1019644</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello we recently learned about diophantine equations and how to use euclidean algorithm to solve it, but i am kind of really stuck!\r<BR>\n" );
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document.write( "find all solutions to each of the following Diophantine equations:<BR>\n" );
document.write( " 24x+63y=99\r<BR>\n" );
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document.write( "how could i use the algorithm to solve this? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #636366 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=636366\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First find the GCD using the Euclidean algorithm,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=63=2%2A24%2B15 ALIGN=MIDDLE  ALT=\"63=2%2A24%2B15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24=1%2A15%2B9 ALIGN=MIDDLE  ALT=\"24=1%2A15%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15=1%2A9%2B6 ALIGN=MIDDLE  ALT=\"15=1%2A9%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9=1%2A6%2B3 ALIGN=MIDDLE  ALT=\"9=1%2A6%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6=2%2A3 ALIGN=MIDDLE  ALT=\"6=2%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=GCD=3 ALIGN=MIDDLE  ALT=\"GCD=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Using back substitution,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=9-1%2A6 ALIGN=MIDDLE  ALT=\"3=9-1%2A6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=9-1%2815-1%2A9%29=15-2%2A9 ALIGN=MIDDLE  ALT=\"3=9-1%2815-1%2A9%29=15-2%2A9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=15-2%2824-1%2A15%29%29 ALIGN=MIDDLE  ALT=\"3=15-2%2824-1%2A15%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=8%2A24-3%2A63 ALIGN=MIDDLE  ALT=\"3=8%2A24-3%2A63\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=8 ALIGN=MIDDLE  ALT=\"n=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-3 ALIGN=MIDDLE  ALT=\"m=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=24 ALIGN=MIDDLE  ALT=\"a=24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=63 ALIGN=MIDDLE  ALT=\"b=63\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=99 ALIGN=MIDDLE  ALT=\"c=99\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=GCD=3 ALIGN=MIDDLE  ALT=\"GCD=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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