document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=436086>Question 436086</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find integers x and y satisfying 966x + 686y = 70 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #301708 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=301708\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note that all the coefficients are divisible by 14, so we can divide through by 14:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=69x+%2B+49y+=+5 ALIGN=MIDDLE  ALT=\"69x+%2B+49y+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This can be rewritten as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49%28x%2By%29+%2B+20x+=+5 ALIGN=MIDDLE  ALT=\"49%28x%2By%29+%2B+20x+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. It follows that x+y &#8801; 0 (mod 5).  Suppose that x+y = 5. If this is so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49%285%29+%2B+20x+=+5 ALIGN=MIDDLE  ALT=\"49%285%29+%2B+20x+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20x+=+-48%285%29 ALIGN=MIDDLE  ALT=\"20x+=+-48%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> x = -12. Replacing x, we obtain y = 17. It checks that 966(-12) + 686(17) = 70. </SPAN>\n" );
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