document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1035769>Question 1035769</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all values of p and q such that 3p+7q=1 and 5p=14q+53 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #650413 by </B><A HREF=/tutors/aboutme.mpl?userid=fractalier><B>fractalier(6550)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fractalier><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=fractalier><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=650413\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> From the system<BR>\n" );
document.write( "3p+7q=1<BR>\n" );
document.write( "5p=14q+53<BR>\n" );
document.write( "we can solve by doubling the first one, solving for 14q and plugging that into the second one, like this...<BR>\n" );
document.write( "6p + 14q = 2<BR>\n" );
document.write( "14q = -6p + 2<BR>\n" );
document.write( "5p = (-6p + 2) + 53<BR>\n" );
document.write( "5p = -6p + 55<BR>\n" );
document.write( "11p = 55<BR>\n" );
document.write( "p = 5<BR>\n" );
document.write( "Now plug that in to the top one and get<BR>\n" );
document.write( "3(5) + 7q = 1<BR>\n" );
document.write( "15 + 7q = 1<BR>\n" );
document.write( "7q = -14<BR>\n" );
document.write( "q = -2<BR>\n" );
document.write( "(5, -2) is your solution. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );