document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=464737>Question 464737</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A two digit number is obtained by either multiplying the sum of the digits by 8 and adding 1, or by multiplying the difference of the digits by 13 and adding 2. Find the number </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #318398 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=318398\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let xy be the unknown number. ==> x = tens digit, and y = ones digit.\r<BR>\n" );
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document.write( "Then from the given, 8(x+y) + 1= 10x + y, and 13(x-y) + 2 = 10x + y.\r<BR>\n" );
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document.write( "<==> 2x - 7y = 1 and -3x + 14y = 2\r<BR>\n" );
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document.write( "Proceeding with the method of elimination, we get x = 4 and y = 1.  (Check these solution against the original system!)\r<BR>\n" );
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document.write( "Therefore the number is 41. </SPAN>\n" );
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