document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183263>Question 1183263</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "Find positive intergers x and y that satisfy the rule 9x + 6y = 90<BR>\n" );
document.write( "Thanks \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #813503 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=813503\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%2B6y=90 ALIGN=MIDDLE  ALT=\"9x%2B6y=90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B2y=30 ALIGN=MIDDLE  ALT=\"3x%2B2y=30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "x and y are positive integers, so 2y is an even number; and 30 is an even number.<br><BR>\n" );
document.write( "That means 3x must be an even number; and that means x is a (positive) even integer.<br><BR>\n" );
document.write( "Find the solutions by enumeration.<br><BR>\n" );
document.write( "x=2: 6+2y=30; 2y=24; y=12  (x,y)=(2,12)<BR>\n" );
document.write( "x=4: 12+2y=30; 2y=18; y=9  (x,y)=(4,9)<BR>\n" );
document.write( "x=6: 18+2y=30; 2y=12; y=6  (x,y)=(6,6)<BR>\n" );
document.write( "x=8: 24+2y=30; 2y=6; y=3  (x,y)=(8,3)<br><BR>\n" );
document.write( "Higher values of x will yield zero or negative values of y, so that list of 4 solutions is the complete list.<br><BR>\n" );
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